Julian Assange appeared at the high court in London yesterday for the first day of the latest stage of his fight against extradition to Sweden over sex allegations. The WikiLeaks founder will be back in court this morning for what is expected to be the final day of the hearing.

Clare Montgomery QC, speaking for the Swedish authorities, is expected to argue that the decision to allow Assange to be extradited at the last stage of this legal process was correct. They will contend that the European arrest warrant under which Assange was arrested is nothing less than fair, accurate and proper and there is no justification for an inquiry into the validity or accuracy of the statements it contains, as Assange's legal team suggested yesterday.

Judgment is expected to be reserved, so a ruling might not be made public for days or weeks. If he loses, Assange could take his case to the supreme court, although permission to appeal to the supreme court would only be granted on a point of law considered to be of general public interest.

Here are the key points from yesterday's hearing:

• Assange is claiming that the European arrest warrant that led to this hearing contained "fundamental misstatements" of what occurred in Stockholm last August. It falsely claims he used violence and "acted in a manner to violate sexual integrity", Assange's legal team said.

• The WikiLeaks founder's team claimed that his encounters with two women who made complaints against him involved consensual sex and would not be considered crimes in England. Ben Emmerson QC, his barrister, admitted that the women involved may have found Assange's behaviour "disreputable, discourteous, disturbing, or even pushing towards the boundaries of what they were comfortable with" – discussing, for example, Assange's initiating sex with one woman while she was asleep – but maintained that no crime had been committed under UK law.

• Emmerson also claimed that the use of the European warrant was "disproportionate", as there were other means available to obtain Assange's assistance in the Swedish investigation.

You can read all our coverage of yesterday's hearing as it happened here, while, in the Guardian today, Robert Booth sums up the day's events.

Assange's barrister set out the accusations against Assange in graphic detail yesterday, but as Robert points out Assange's case against extradition does not hinge on whether he accepts these versions of events and testimonies relating to other incidents because there are no charges against him, Emmerson said. Rather, the barrister said, it was a question of whether the arrest warrant in connection with the allegations is valid on "strict and narrow" legal grounds.

Assange – who is appearing before Lord Justice Thomas and Mr Justice Ouseley – is wanted to answer questions on three allegations of sexual assault and one of rape involving the women, referred to as AA and SW, in Stockholm last August. He denies wrongdoing.

Robert Booth is at the Royal Courts of Justice, where the usual posse of news cameramen have gathered to record Assange's court entrance. A few more protesters against the legal proceedings have also turned up. One placard reads: "Julian Assange dacks the rich and powerful", Australian slang for pulling down their trousers.

John Pilger, the campaigning leftwing journalist and Assange ally, got a round of applause as he arrived at the court this morning. He did not look amused at his role as warm-up act.

Julian Assange has arrived at the high court. As yesterday, he said nothing but smiled and nodded to his applauding supporters. Robert Booth took a picture.

Assange is in good spirits in court four: kisses on both cheeks for his lawyer Gareth Peirce. But the QC for Sweden, Clare Montgomery, is limbering up.

Mark Summers, who is acting for Julian Assange, says the WikiLeaks founder is suspected "with probable cause" in Sweden but this comes before any charges – so he is not "accused", so the European arrest warrant is not valid

The argument is currenlty revolving around whether the Swedes are going to prosecute Assange or only want to question him.

Mark Summers, acting for Assange, says this about the European arrest warrant: "There was from the outset of this case an easier way to proceed. A more proportionate way."

Europe requires a proportionality check on warrants, Summers says. Is there "an approach less onerous for the person sought and the prosecuting authority"?

Lord Justice Thomas says "looking at this case ... a huge amount of time and publicity has been given that is in no one's interest".

Judicial authority is independent of both the executive and the parties, Assange's side is arguing – so is the Swedish prosecutor allowed to issue a European arrest warrant?

If this argument is right, the judge replies, "it drives a substantial wedge into the application of the European arrest warrant".

Clare Montgomery QC is opening for Sweden now.

Clare Montgomery, for Sweden, starts by saying public prosecutors have long issued arrest warrants that were processed by UK courts as grounds for extradition.

Clare Montgomery is sniping at the length of the Assange side's skeleton argument, saying: "I lost the will to live." Ben Emmerson QC, Assange's barrister, is not impressed.

The judge is worried about "undermining public confidence" in the European arrest warrant regime if the definition of judicial authority becomes too wide.

The judge is implying that there is a question over how much the Assange arrest warrant was issued by an arm of the Swedish state, and how much by an independent judicial authority. He is only hinting at that, but it might interest conspiracy theorists who believe US pressure on Sweden precipitated the extradition request.

The court is now debating whether the Assange case is sufficiently developed towards prosecution as to be suitable for a warrant. Sweden's legal team say: "The fact it is in the investigative phase doesn't matter. What matters is the underlying motive of the request."

Clare Montgomery attempts to undermine the Assange team's arguments, saying: "Extradition offence means the conduct complained of. It has nothing to do with the evidence."

Montgomery, acting for Sweden, says there is "nothing to suggest the prosecutor has intent to bring the case as described in some of the witness statements rather than as put in charges".

One of the Assange team's key contentions is that the differences between what is outlined in the witness statements and what is in the European arrest warrant means the warrant is not valid.

On to the testimonies about Assange – Montgomery, acting for Sweden, says she sees them very differently. "They are describing circumstances in which they [the alleged victims] did not consent without coercion. They were coerced by physical force or were trapped."

Assange's alleged rough conduct, breaking one alleged victim's necklace and lying on top of her, do not add up to consent, she says.

The Associated Press news agency sums up some of the earlier exchanges:

Ben Emmerson QC [Julian Assange's barrister] today attacked the way in which the extradition request was made, arguing that public prosecutors are not allowed to issue European arrest warrants. The prosecution rejected the accusation and it was greeted with scepticism from one of the judges.

The first allegation against Assange "relates to actions to which nobody suggests she [one of the alleged victims] was positively consenting", says Montgomery.

Montgomery, acting for Sweden, says: "Assange lying on top of her [tried] to force his unprotected penis into her, which she did not want, and held her arms."

Judge Thomas says: "We are not concerned with whether this is a good case or a bad case but whether what is charged amounts to a crime."

Helena Kennedy QC has entered court and is sitting on the same bench as Assange.

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Montgomery says Assange agrees that he knew that AA had rejected sexual invitations from him.

Montgomery says there is "evidence that she [SW] was penetrated while asleep ... in a way she made clear she did not consent to" if unprotected.

The Press Association news agency has filed its first report on this morning's session.

According to Clare Montgomery QC, acting for the Swedish authorities, Julian Assange faces genuine accusations of "non-consensual, coerced sex".

Statements made by the two women who have accused Assange of sexual misconduct – one of whom said she was "roughed up" – plainly showed they did not freely consent, Montgomery said.

Montgomery said it was "perfectly plain" that the women had made allegations of non-consensual, coerced sex. That was "clearly the only legitimate inference one can draw from the plaintiff's statements".

She told Lord Justice Thomas and Mr Justice Ouseley that the women described circumstances "in which they did not freely consent without coercion" but agreed to sex because of physical force, or consented "already having been trapped into a position where they had no choice, and they submitted to Mr Assange's attentions".

They had "let him continue", said Montgomery. "This is non-consensual. It is coerced, and the words used - 'I let him' - means non-consent," said the QC.

She referred to a statement made by AA in which she said: "I didn't make a free choice. He had already roughed me up by tearing off my clothes and breaking my necklace."

Montgomery said earlier that the fact AA voluntarily shared a bed with Assange four days after their first encounter "did not mean she consented" to his pressing his penis against her in that first encounter.

She tells the court that one of the alleged victims said that Assange "preferred virgins since he was the first to impregnate them".

More from the Press Association's report.

Clare Montgomery QC, acting for Sweden, argued that AA had been a victim of "coercive violent sex". She said:

They [the statements] are clearly describing coercive, violent sex of the sort where the court would be entitled to infer there was no consent and Mr Assange didn't believe there was any. The [first] charge relates to actions [to] which nobody suggested she was positively consenting.

Montgomery said the woman had later made her feelings "crystal clear" to a friend, saying "what had happened had gone beyond the limit of what she consented to".

She said that AA also complained that Assange had "broken a condom" and added: "The complaint is unprotected sexually intercourse where consent had only been given to protected intercourse."

On one night the first woman had agreed to share a single bed with Assange but not to be sexually "touched", Montgomery added.

Prosecutors alleged that the woman's "sexual integrity" had been "violated", judges were told.

Robert Booth has sent his summing up of this morning's exchanges.

The case laid out by Clare Montgomery QC, appearing for the Swedish authorities, is that Julian Assange must be extradited to Sweden to face the accusations of rape and sexual assault, because the prosecutors' case against him clearly alleges that there was no consent during a string of sexual encounters in Stockholm last August.

Montgomery said the charges set out on the European arrest warrant and supported by witness statements amount to valid allegations for which the cross-border warrant is appropriate.

Assange's side had yesterday argued there was a discrepancy between the allegations of rape, sexual molestation and unlawful coercion set out in the warrant and the witness statements of the two women who complained and so the warrant should not be supported.

Before rehearsing in graphic detail the allegations against the 40-year old Australian, Montgomery told the court the definition of an extradition offence "means the conduct complained of. It has nothing to do with the evidence."

Lord Judge Thomas appeared to support that position saying: "We are not concerned with whether this is a good case or a bad case but whether what is charged amounts to a crime."

Montgomery said the witness statements of the two women, known as AA and SW, who complained about Assange "describe circumstances in which they did not freely consent without coercion. They were coerced either by physical force or they were trapped into a situation where they had no choice."

She described how Assange "roughed up" one woman, broke her necklace and pressed his penis against her. In this case, she said, her consent "may not have been a free choice". Montgomery said:

AA says in her case the prelude to the offence was Mr Assange ripping her clothes of, breaking her necklace, her trying to get dressed again and then letting him undress her.

He then had sex with her after pinning her arms and trying to force her legs apart to insert his unprotected penis, which she did not want, Montgomery said.

In another incident four days later with the same woman Assange undressed and pressed his penis against her. "The fact she voluntarily shared a bed with him did not mean she consented," said Montgomery.

Montgomery said SW had told a friend Assange "said he preferred virgins as he felt he could be the first to impregnate them".

Earlier, Assange's legal team had advanced more arguments as to why the European arrest warrant was not valid. Mark Summers questioned whether the Swedish prosecutor could be considered a "judicial authority [which] is independent of both the executive and the parties" and therefore able to issue the warrant.

Lord Justice Thomas said that many prosecuting authorities in Europe issue European arrest warrants, and that if Assange's argument was right "it drives a substantial wedge into the application of the European arrest warrant".

By contrast, when Montgomery argued that prosecutors can issue such warrants and have done so for many years, the judge warned of "undermining public confidence" in the warrant system if the definition of judicial authority was drawn too wide.

Summers also said Assange was "suspected with probable cause" in Sweden, but because this stage in an investigation comes before a charge and therefore before him becoming "accused", the arrest warrant was not valid.

The case continues this afternoon.

The case has started again for the afternoon. Alexi Mostrous tweets:

A foreign reporter just got a VERY scary shock after taking photo in court. Judge made him stand, told if u do it again you go to prison

More from the Press Association news agency.

Clare Montgomery QC, speaking for the Swedish authorities, said the evidence was "absolutely clear" in relation to the fourth charge – the allegation that Assange raped SW. Montgomery said:

The evidence is absolutely clear that this complainant may be legitimately described as given evidence that she had been penetrated whilst asleep. Furthermore, being penetrated in a way which [it] is absolutely clear ... she had not consented to, namely unprotected. It is doubly clear there is no consent.

Montgomery said the fact that the woman may later have agreed to let Assange continue did not change the "initial" act. "She may later have acquiesced," said Montgomery. "That didn't make the initial penetration anything other than an act of rape."

Montgomery said SW had later told a friend that Assange "had unprotected sex with her when she slept". SW had also told the friend Assange "wanted to impregnate women" and "preferred virgins because he would be the first to impregnate them", as mentioned earlier.

She told the friend she had been "shocked and paralysed" and had "not really understood at first what was happening", said Montgomery. SW's boyfriend had told police that "this is a woman who never had unprotected sex", judges heard.

Montgomery is now detailing the EU framework decision on the European arrest warrant as a rebuff to the Assange team's contention that a charge is needed first before a suspect can be extradited.

Montgomery says the EU directive "deliberately does not identify any point in the process" when the warrant can be issued. "It is deliberately vague," she says.

Montgomery says the allegations against Assange are valid for the European arrest warrant. It lists "concrete offences with reasonable specifics" in "unmistakable language".

Regarding the most serious allegation, that Julian Assange had sex with SW while she was asleep, the Associated Press reports that Clare Montgomery, for the Swedish authorities, attacked Ben Emmerson, Assange's barrister, for quoting testimony stating that "she let him continue". Montgomery accused Emmerson of "effectively winding the law on consent back to the 19th century", adding:

At best, the words "I let him" amount to submission, not free consent.

Robert Booth writes from the high court that the way the case is developing in Clare Montgomery's submission on behalf of the Swedish prosecution authority suggests that Julian Assange's future - freedom from house arrest or extradition for questioning - will rest on the application of the controversial and complex European arrest warrant system.

The details of the allegations in the case are vividly clear and have been rehearsed here in court four but they are not the issue the two judges are wrestling with in what often sounds like an academic comparative law exercise.

Among other things, the judges are being taken on a tour of variation in criminal procedure in the EU and in particular when a charge is firm enough for a warrant to apply; how different states use different authorities to press charges; and language, for example whether suspicion, accused and other terms mean the same thing in different languages in different systems.

The complexity of all this is a feature of EU law, it seems: the clash and confusion with member states' different systems when the intent of a single EU system was to simplify.

Even the judges seem to be feeling overwhelmed by the range of variation between say Belgium, France and Germany. So it is no surprise that Assange's destiny is becoming no more clear as the case winds on. Does the supreme court loom or is this case not sufficiently in the public interest?

This is getting baroque: "Assange is accused in a popular sense if not in a technical sense," says Montgomery.

The Press Association notes details told to the court about how Assange met the two women.

The first woman, AA, worked for a political group that had invited Assange to Sweden to give a lecture, the court heard. She said that Assange could stay in her apartment in Stockholm, lawyers said.

She had "thrown a crayfish party" in Assange's honour and had sent a tweet saying "... with the world's coolest people, it's amazing ... "

Lawyers said the second woman, SW, became captivated with Assange when she saw a television interview with him. She had found out where he was speaking then attended the talk.

She had "helped" by buying a computer cable for Assange, attended an "intimate lunch" with him and Assange had flirted with her.

The first woman told police that Assange's physical advances were "initially welcomed" but "then it felt awkward" since he was "rough and impatient", Assange's lawyers told judges.

She described one encounter by saying that Assange "continued to have sex" and "she just wanted to get it over". Talking about another encounter, she described Assange's behaviour as "very strange".

The woman told police that "Assange tried to make sexual advances towards her every day after that evening when they had sex"'. She had rejected Assange, which he "had accepted".

"Her words may indicate she was not particularly enjoying what was going on, but they certainly do not go anywhere near what we would regard in this country as lack of consent," said Ben Emmerson QC, for Assange, yesterday.

Lord Justice Thomas is vexed about the unwillingness of Sweden to allow Julian Assange to be interviewed without extradition in the spirit of "EU co-operation".

He asks: "Why are we precluded from acting with sense in this European Union when the commission talks about [judicial] co-operation?"

Ben Emmerson, Assange's barrister, says the idea of isolating a moment of lack of consent in an encounter that was consenting both before and after "is crazy".

He says: "A lot of what has been said to your lordships is simply a waste of time."

He says, a little facetiously, that Clare Montgomery, for Sweden, posited "some very progressive and some may say desirable definitions of consent".

From the high court, Robert Booth says Ben Emmerson is talking in a deliberately emphatic manner in an attempt to change the atmosphere of the court in Assange's favour.

Emmerson goes into detail about Assange's sharing a single bed with a woman – to laughter in the court.

The question is did she consent to his getting an erection, says Emmerson, Assange's barrister.

"The question is what he does with it," says Mr Justice Ouseley.

Emmerson, for Assange, says of his client:

He's lying beside her in a single bed, my lord. Men will get erections involuntarily during a night's sleep. In a single bed with a man there's a strong possibility she will come into contact with an erect penis.

The judge replies: "I agree."

Emmerson (left) is now restating Assange's case that the charges on the European arrest warrant are not a proper version of the claimants' allegations.

Ben Emmerson QC, for Assange, says: "The clearest possible facts have been concealed through the terminology of the warrant. That is wrong."

Emmerson, Assange's barrister, says one complainant felt "railroaded" by police and colleagues and only wanted Assange to get a blood test, not to press charges.

The Italian journalist taking a photo in court earlier provoked a warning from the judge that members of the media and the public attending court can "tweet – but not snap", the Press Association reports.

Alessandro Carlini, a freelance writer, had his mobile phone confiscated and was told that he had committed contempt of court and under normal circumstances would be taken down to the cells until legal representation could be provided and the matter dealt with.

Alessandro apologised in court and said later he had mistakenly pressed "the wrong button" on his mobile.

Lord Justice Thomas ordered him to stand up in the crowded court after the midday break and warned him he was committing contempt of court.

Thomas said the media were now allowed to use mobiles and other technology to keep the public informed of court proceedings, but "it has always been made very clear photographs are not to be taken".

The judge said he understood Alessandro may not have been entirely to blame, but the case should serve as a warning to everyone that in future such conduct would lead to contempt proceedings.

AA, who slept with Assange, "did not even say she had been exposed to abuse; she didn't even want to go to the police," says Emmerson.

Mark Summers is speaking now for Assange: "The prosecutor has never sought to explain why she has not engaged all other mechanisms [ie other than extradition] to progress this investigation ... The reason there is a stand-off is entirely of Sweden's making. What a waste of time."

And that's it. The judgment will be reserved so we will not be getting it today.

Lord Justice Thomas said there would be another hearing to hand down the judgment. He thanked both sides and said: "We will take time to consider the numerous arguments and authorities."

It is estimated that it could be at least three weeks before the judgment is handed down.

The high court has reserved judgment on whether Julian Assange should be extradited to Sweden to face sex crime allegations. A judgment is not expected for at least three weeks.

Here are the key points from today's hearing:

• Clare Montgomery QC, acting for the Swedish authorities, said that public prosecutors have long issued arrest warrants that were processed by UK courts as grounds for extradition. She said it did not matter that Assange was wanted for questioning, rather than facing charges. The wording of the warrant was deliberately vague on this point, she said. She dismissed the Assange team's claims that there were crucial differences between the complaints in the witness statements and those in the warrant, saying there was nothing to suggest the prosecutor was going to use the witness statements as the basis of the case rather than the warrant.

She said that Assange's alleged victims "did not consent without coercion", spelling out the accusations in detail. In the case of AA, "nobody suggests" the alleged victim "was positively consenting", with "Assange lying on top of her trying to force his unprotected penis into her, which she did not want". In the case of SW, there is "evidence that she [SW] was penetrated while asleep ... in a way she made clear she did not consent to" if unprotected. Montgomery said the fact that the woman may later have agreed to let Assange continue did not change the "initial" act. "She may later have acquiesced," said Montgomery. "That didn't make the initial penetration anything other than an act of rape."

• Assange's team argued that there were "more proportionate" ways to proceed than using the European arrest warrant. Mark Summers, for Assange, questioned whether the Swedish prosecutor could be considered a "judicial authority [which] is independent of both the executive and the parties" and was therefore able to issue the warrant. But Lord Justice Thomas said many prosecuting authorities in Europe issued European arrest warrants.

Ben Emmerson QC, acting for Assange, said the idea of isolating a moment of lack of consent in an encounter that was consenting both before and after "is crazy". Yesterday he argued at length that Assange's behaviour may have been "disreputable, discourteous, disturbing, or even pushing towards the boundaries of what [the alleged victims] were comfortable with" but was not a crime in the UK.

• Thomas appeared to support Montgomery's position that the definition of an extradition offence "means the conduct complained of. It has nothing to do with the evidence." The judge said: "We are not concerned with whether this is a good case or a bad case but whether what is charged amounts to a crime."

Assange, the founder of WikiLeaks, is wanted to answer questions on three allegations of sexual assault and one of rape involving AA and SW, in Stockholm last August. He denies wrongdoing.

Robert Booth will be filing his full story from the hearing soon – you will be able to read it here. Thanks for all your comments.