It is a humid July day in Strasbourg, and inside the Louise Weiss Building it feels like the start of school term. Journalists and politicians, assembled for the opening session of the European Parliament, are greeting each other like old friends outside the main debating chamber, known in a typical piece of EU jargon as the Hemicycle. Here, in the glass and pine atrium of this imposing cylindrical edifice - Britain's signature contribution to which is a garish floral carpet in the staff bar that bears more than a hint of cross-Channel ferry - you might spot Daniel Cohn-Bendit, the ex-revolutionary French Green and the closest thing the EU has to a pop star, strolling around with his entourage of admirers. Or Nigel Farage, the leader of the UK Independence Party (Ukip), as he lambasts the rise of "the European military superpower" in front of assembled TV cameras. The atmosphere here, compared to Westminster, is open and collegiate.

Hidden away, however, at the end of a winding corridor on the top floor of an adjoining administrative block, a strange meeting is taking place. Convened by Andreas Mölzer of Austria's immigrant-hating Freedom Party, it is a meeting of the non-inscrits, the "non-attached" MEPs, from parties that have failed to make it into one of the mainstream coalitions. Aside from a few mavericks, such as Diane Dodds of Northern Ireland's Democratic Unionist Party, this means the far right - including two of Britain's new crop of MEPs: Nick Griffin and Andrew Brons of the British National Party. Although the BNP is not a traditional fascist party or Nazi organisation, its constitution commits it to "restoring . . . the overwhelmingly white make-up of the British population that existed in Britain prior to 1948".

Earlier in the day, having travelled across France by car, Brons and Griffin had ­commanded the attention of the British press corps when they made their first, tentative appearance at the Hemicycle. Now they are due at a more furtive gathering. I remove my bright yellow press badge, slip it into my pocket, and watch an in­ternational assembly of bigots file into the conference room: Krisztina Morvai of Jobbik, the gypsy-hating Hungarian party with its own private, uniformed militia; the French Holocaust denier Jean-Marie Le Pen of the Front National, along with his daughter Marine; assorted podgy members of Belgium's Flemish Interest and the Netherlands' Party for Freedom, both of which are anti-Islam

Then, ambling down the corridor, come Griffin and Brons, accompanied by Simon Darby, the BNP's press officer, Jackie Griffin (wife of Nick) and a large minder in an ill-fitting suit. Outside the conference chamber stand a few men and women wearing tourist passes and speaking in French. One of them, barely out of his teens, clutches copies of a magazine titled Identitaires. This is the in-house magazine of the French sect Bloc Identitaire, which runs a Europe-wide "news" agency called Novopress that distributes far-right propaganda. Griffin walks up and shakes his hand. "We've met before, haven't we?" he says. They make slightly awkward conversation, the young man explaining that his group has "a good relationship" with the Front National. Griffin makes a vague offer to help get the magazine translated into English - "for those of us who are interested in identity", he says, sighing. They then follow the remaining members into the conference room.

The collection of oddballs on the other side of the door is the dirty secret of the European Parliament. In the family of nations that the parliament supposedly represents, the far right has long been the foul-mouthed elderly relative. In a way, Britain has simply caught up with the rest of Europe, which has grudgingly accepted the presence of a few extremists as part of the proportional representation electoral system.

But it is also part of a more disturbing narrative. Lívia Járóka, a Hungarian MEP of Roma origin, is particularly concerned at the support gained by Jobbik, which came third in her country's elections. "[Jobbik's success] has a lot to do with the current economic crisis. People feel very unsafe, so they are ready to accept answers with no real base in fact." She feels the best way to challenge their arguments is to confront them directly.

"Rather than ignore the far right, we should try to show that what they are claiming is complete empty propaganda."

Little more than a month since the BNP was elected, its victory looks decidedly hollow. Its negotiations with other far-right parties, conducted at the parliament's other base in Brussels over the past month, have failed to round up enough allies to form an official coalition of MEPs. As a result, they have been denied any extra funding beyond the standard salary (a generous £63,000) and staffing allowance, nor will they have access to any influential positions, such as committee chair or vice-president of the parliament. At most, they will be able to obtain seats on parliamentary committees and use them as a platform to make grandstanding statements - assuming anyone is still listening in six months' time. Griffin, who believes climate change is "bollocks", has already got a seat on the environment committee.

While the BNP and its closest allies remain isolated, however, there has been a wider shift to the right since their electoral successes in June, and some ultranationalist elements have managed to insinuate themselves into the mainstream. This is largely thanks to the actions of two British parties - the Conservatives and Ukip.

Under the direction of David Cameron, the Tories quit the centre-right European People's Party to form a new, Eurosceptic coalition, the European Conservatives and Reformists (ECR). Their main partner is Poland's socially con­servative Law and Justice party, which has a well-documented record of anti-gay rhetoric. Its leader in the European Parliament, Michal Kaminski, was a member of the far-right, anti-Semitic National Revival of Poland in the late 1980s. In 2001, the US-based Anti-Defamation League accused him of having attempted to

stop the commemoration of a wartime pogrom against Jewish people in the Polish town of Jedwabne. Despite this, the Tory MEP Daniel Hannan this month described Kaminski on his blog for the Daily Telegraph as "a Thatcherite: a sturdy Polish patriot who is nonetheless, in outlook, almost a British Tory".

Not all of Hannan's colleagues share this view. Edward McMillan-Scott, a committed pro-­ European Tory MEP of 25 years, respected across the political divide, was expelled from the Tory group on 15 July when he stood against Kaminski in an election for vice-president of the parliament, and won. Kaminski was the ECR's official candidate for one of the EU's 12 vice-presidential posts, which are divided between the coalitions in what parliamentary insiders cheerfully refer to as a "stitch-up". EU etiquette frowns on MEPs who rock the boat by opposing members of their own coalitions.

Describing himself to me as a "loyal Tory", who spent the 1980s working in Poland with reformist groups, McMillan-Scott regrets going against the wishes of his party, but says he was compelled to do so by what he calls "the rise of respectable fascism" in Europe. He sees the alliance as a grave setback for Cameron's attempts to decontaminate the Conservative brand. "This is where the modern Conservative Party has to tread very carefully," McMillan-Scott tells me. "David Cameron has done a remarkable job in repositioning the party on most things. Its attitude to gays, or the environment, for example, has fundamentally changed. There's just the question of these links [to right-wing extremists in Europe] and one can't close one's mind to it."

To the Labour MEP Michael Cashman, this shows a lack of leadership on Cameron's part. "It suggests that Cameron is unable to control his MEPs and has shifted them where they want to go, which is further to the right."

Ukip's new friends are even more unsavoury. The party's major partner in the Europe of Freedom and Democracy group, formed at the beginning of this month, is Italy's Lega Nord, which, despite being part of Silvio Berlusconi's governing coalition at home, wants autonomy for northern Italy and has a track record of xenophobic and anti-gay statements. Other members of the group - described by Searchlight's Europe correspondent Graeme Atkinson as a "far-right-lite" coalition - include Greek and Slovak extreme nationalists. Nikki Sinclaire, Ukip's first openly lesbian MEP, concedes to having "reservations" about her new allies. "All the parties [of Freedom and Democracy] have signed up to a statement saying they oppose all forms of discrimination. But it is difficult. I think this is going to evolve over the next couple of months."

The Freedom and Democracy coalition is in part a shrewd move to block the more extreme far-right parties, such as the BNP, from forming

a coalition - Lega Nord was initially touted as a possible partner for the BNP. However, it creates a potentially more toxic alternative. Most of the British MEPs are now in alliances with extreme conservatives, with whom they will be seeking a common position on a range of issues, from equality legislation to the Convention on Human Rights.

Labour, meanwhile, faces severe problems. The party has only 13 MEPs left in the parliament - level with Ukip. The corresponding drop in funding (which is allocated according to the number of MEPs elected) has led to redundancies among auxiliary staff. Yet, despite the BNP's electoral success being largely down to a collapse in the Labour vote - even if most core Labour voters wouldn't dream of supporting the BNP, they helped it by staying away from the polls - none of the Labour MEPs I spoke to was willing to look beyond short-term causes. I suggested to Cashman, a former EastEnders actor who now represents the West Midlands, that Labour had lost the support of its working-class base. "Bullshit. The ascent of the BNP, along with the ascent of Ukip, can be traced directly to the timing of the Westminster expenses scandal," he said.

Richard Corbett, who lost his seat in Yorkshire and the Humber, where the BNP's Brons was elected, narrows it down even more. "The final nail in the coffin was Hazel Blears resigning [from the cabinet] the day before the election. It was a kick in the teeth to thousands of volunteers in the party and caused maximum damage - in our case, the difference was only a few thousand votes, so she really made that difference."

The damage now extends beyond the Labour Party. Griffin, Brons and their European allies may have failed to form an official grouping, but they share a strategy of trying to play down the overtly racist rhetoric and to influence mainstream debate. "We are treated like pariahs," Marine Le Pen tells me when I ask her what the Front National has in common with the BNP. "The traditional parties try to give us a completely warped image."

I eventually meet Griffin an hour or so after the majority of Britain's 72 MEPs have gathered for a drinks reception hosted by Glenys Kinnock, Britain's Europe minister. Griffin and Brons were pointedly not invited. The snub evidently hurt: throughout the opening week of parliament, journalists were treated to Griffin's witty riposte: "I would not want to share a drink with Glenys Kinnock. She is a political prostitute, simple as that."

Despite fears that the BNP would try to gatecrash the party, Griffin and Brons stayed away. Instead, they returned for a few hours to their "reasonably priced" hotel on the edge of the city, a low-budget dormitory surrounded by decrepit industrial buildings, where Jobbik's Krisztina Morvai also stayed.

When we meet in a busy lobby back at the parliament, the pair come across as rather shambolic. Brons, a retired teacher who used to be in the National Front, burbles along in conversation, quoting de Tocqueville and Voltaire. Griffin has a gift for the soundbite but in longer conversations tends to stare at the floor and rant circuitously. I get lost for a while during a passionate discourse on the genetic similarities of human beings to chimpanzees - and why this means we're all bound to kill each other one day unless we maintain ethnic purity. What is interesting about his language is the way in which he manipulates the fears of a declining 21st-century industrial society. He talks of shadowy "global businesspeople" (as opposed to a global financial system), presents human cultures as endangered species (rather than as products of our collective activities), and refers to the apocalyptic threat of peak oil (but not, as we know, climate change).

The suggestion that Britain has benefited from immigration is dismissed as "self-hating racism", but to avoid accusations of racism on his own part, Griffin takes cultural relativism to an extreme. He deplores the "Islamification of Brit­ain", but says Muslims are free to behave as they like "in their own countries. We don't have a right to interfere". Indeed, in his maiden speech, given during a parliamentary debate on Iran, Griffin appeared to defend President Ahmadinejad's regime, describing the pro-democracy pro­tests as a cover for "a third illegal and counterproductive attack by the west on the Muslim world".

Although the BNP's view of society makes no class distinctions, Griffin appeals to "working-class Britons" when it suits him. One word that crops up repeatedly in his analyses is "elite" - as in "the EU is an elite project which has no connection with reality". The other place I notice the use of the word that day is in an email to members of the BNP's mailing list, purporting to come from a "Chairman Nick Griffin MEP". It offers readers a chance to make a donation and become a "Gold member". "Gold members are the 'elite' of the Party," the email says. "They go that extra mile and quite rightly display their Gold membership badge with pride at Party meetings and events." The badge "also makes a superb addition to any type of clothing, whether a suit or casual".

Despite his party's commitment to British withdrawal from the EU, Griffin tries to strike a conciliatory tone. "We're going to engage here, because although we believe Britain should be withdrawn, you can't have this many people together and not come up sometimes with something that is actually a good idea."

I had had an insight the previous day into the far right's idea of what it means to "engage" at the meeting of non-inscrits, the aim of which was to nominate one group member who could speak on behalf of the others at official engagements. Waiting outside the meeting, I listened as the murmured voices became louder and more strained. Then a row erupted. It went on and on. A posh English voice filled the corridor, followed by the smoker's rasp of Marine Le Pen, and then that of her father, shouting in French. Le Pen Sr yelled at the chair of the meeting: "You are a civil servant! I am an elected representative!" The chair replied: "Monsieur, if you carry on like this then

I will have to close the session."

Soon after that, the voices stopped. A group of interpreters exited from a side door, laughing. As they passed, I heard one say to the others, mockingly, "And they say dictatorship would be a bad idea . . .".