Boris Johnson has hardened his position on leaving the EU “do or die” by the end of October, as hardline Eurosceptics extended their influence on his faltering campaign to be prime minister.

The frontrunner toughened his Brexit stance as criticism continued over his refusal to answer questions about a police visit to his flat following a loud late-night altercation with his girlfriend, Carrie Symonds.

In a round of interviews designed to put the focus back on his EU policy and away from his personal life, Johnson appeared to signal there was an increasing prospect of a no-deal Brexit three months after he would take office.

Profile Boris Johnson's Tory leadership campaign Show Hide Personal style A late-night altercation between Tory leadership favourite, Boris Johnson, and his partner, Carrie Symonds initially changed the dynamics of Johnson's campaign. He had been either invisible or deliberately sober to the point of dullness, when his usual primary draw to Tory members is a self-created sense of optimism and fun. Much is also made of his supposed broad appeal to the electorate, evidenced by two terms as London mayor. His bizarre claim to make model cardboard buses has raised eyebrows. In most political contests, Johnson’s character – he has lost more than one job for lying, and has a complex and opaque personal life – would be a big issue, but among the Tory faithful he seemingly receives a free pass. It remains to be seen what impact that late-night police visit will have on his chances. Brexit He has promised to push for a new deal while insisting the UK will leave the EU come what may on 31 October, even if it involves no deal. While his hard Brexit supporters are adamant this is a cast-iron guarantee of leaving on that date, elsewhere Johnson has been somewhat less definitive. Asked about the date in a BBC TV debate, Johnson said only that it was 'eminently feasible', although he then went on to tell TalkRadio that the 31 October deadline was 'do or die'. Taxation His main pledge has been to raise the threshold for the 40% higher tax rate from £50,000 to £80,000, at a cost of almost £10bn a year, which would help about 3 million higher earners, a demographic with a fairly sizeable crossover into Tory members. Johnson’s camp insist it would be part of a wider – and so far unknown – package of tax changes. Public spending He has said relatively little, beyond promising a fairly small increase in schools funding, as well as talking about the need to roll out fast broadband across the country. Johnson has generally hinted he would loosen the purse strings, but given his prior fondness for big-ticket projects – London’s cancelled garden bridge, the mooted 'Boris island' airport – perhaps expect more of a focus on infrastructure projects than services. Climate and environment This is unlikely to be a big issue for Conservative party members, and Johnson has not said much on this beyond confirming his general support for the new government target of cutting greenhouse gas emissions to a net zero by 2050. Foreign policy Also unlikely to be a big issue among Tory members, beyond vague platitudes on 'global Britain', it could be a weak spot for Johnson given his poor performance as foreign secretary. He was seen as something of a joke by diplomats – both UK and foreign – and is likely to face more questioning over his gaffe about the jailed British-Iranian woman Nazanin Zaghari-Ratcliffe Peter Walker Political correspondent Photograph: Isabel Infantes/AFP

Johnson first doubled down on his commitment to leaving on 31 October in an interview with Talkradio, saying he was in no way reneging on his firm pledge.

“We are getting ready to come out on 31 October. Come what may,” he said. Asked to confirm this, he added: “Do or die. Come what may.”

He then said he would scrap Theresa May’s withdrawal agreement and seek a completely new deal before then, as minor changes would not satisfy him.

“I mean more than a change,” he said. “It’s got to be, we need a new withdrawal agreement – if we’re going to go out on the basis of a withdrawal agreement.”

Not only has the EU said it will not reopen the withdrawal agreement, but the timetable would be extremely tight as parliament is in recess over the summer and then sitting for about 10 days before party conference season begins. MPs return midway through October, just a few weeks before the deadline.

Johnson then emphasised his position on leaving by 31 October yet again by writing a letter to Jeremy Hunt, his Tory leadership opponent, challenging him to commit to that date “come what may”.

Hunt replied with a dig that Johnson could find out his policy if he turned up to a Sky News head-to-head debate on Tuesday night that Johnson has refused to attend. “Hi Boris, it’s good to talk. But no need for snail-mail, why not turn up to Sky tonight and I’ll give you full and frank answers?#BoJoNoShow,” he tweeted.

Hunt also tried to claim his Brexit policy was similar to Johnson’s but that he would be a more trusted negotiator to deliver changes that could get through the UK parliament. “Who is the person that we trust to send to Brussels on behalf of the British people and come back with a deal, and that has to be someone that they trust, that they’re prepared to talk to, because in the end you don’t do a deal with someone you don’t trust,” Hunt told the BBC in an interview.

In fact, Hunt’s stance is more moderate than that of his rival as he has not committed to leaving on 31 October if he needs more time to do a deal. Johnson also wants to throw out the withdrawal agreement for a new one, while Hunt would be seeking more modest tweaks.

In another sign that Johnson’s campaign was taking a more hardline turn, he appointed Iain Duncan Smith, a veteran Eurosceptic and former Tory leader, as his campaign chief. Johnson also revealed Mark Fullbrook, a business partner of the Australia election guru Lynton Crosby, would be formally joining the team.

Sources close to the campaign said Eurosceptics in the party were increasingly turning the screws on Johnson by warning they would withdraw support for his government if he fails to take the UK out of the EU by 31 October.

One of the 28 “Spartan” MPs who voted against May’s withdrawal deal said they would not tolerate minor changes to the agreement repackaged and sold as a great new deal. He said they were working on the assumption that Johnson was heading for a no-deal Brexit and parliament could either be not consulted or simply ignored.

Johnson appeared to bear out that strategy in his Talkradio interview in which he said he could categorically rule out an extension to article 50, meaning he believes he has a way to stop parliament blocking a no-deal Brexit.

“It would be up to the prime minister of the day. I have myself to decide under the current terms of the extension that we have, to apply for such an extension. And it is up to the EU to decide whether to grant it. At the moment, the law says that the UK is leaving the EU, international treaty law says the UK is leaving the EU on 31 October.”

At the same time, up to a dozen MPs on the centrist wing of the party, such as Ken Clarke and Philip Hammond, have been warning they could bring down the government in a confidence vote together with opposition parties if Johnson tried to exit without a deal.

In an earlier interview on LBC radio, Johnson dismissed the idea his Brexit plans could be hampered by Tory rebels, saying the party was “staring down the barrel of defeat” if it did not deliver a departure plan, which would focus minds.

'It’s an easy audience here': Boris Johnson surfaces at Surrey garden Read more

Johnson has been criticised for hiding during the campaign but he attempted to neutralise that criticism with a series of choreographed campaign visits on Tuesday including a speech to a horticultural society and a walk down a high street in Surrey.

He conducted the round of media interviews and was filmed on the campaign trail, after keeping a low profile for the first part of the campaign and dodging questions over the weekend about the screaming row with his partner that prompted a neighbour to call the police.

He was asked 26 times on LBC about the provenance of a photograph showing him with his partner smiling in a Sussex garden, which appeared on news websites on Monday. However, Johnson refused every time to say whether it was staged, who released it and whether it was recent. “Newspapers will print whatever they are going to print,” he said. “The longer we spend on things extraneous to what I want to do, the bigger the waste of time.”

His mood was subdued at a hustings in Birmingham on Saturday, the day after the story of the row broke in the Guardian, where he told the event’s moderator, Iain Dale, that people did not want to know “about that sort of thing”.

But a film has emerged of him giving a rabble-rousing speech to a private garden party later that day, telling Conservative members that the NHS absolutely needs “reform” and firing them up for a general election by asking them to be ready to “wallop Jeremy Corbyn”.

Play Video 1:17 Boris Johnson tells Tory members NHS 'needs reform' – video

Asked by one party member what he would do with the NHS, Johnson told the crowd the health service was a “crowning glory” but was “not getting the kind of support and indeed the kind of changes and management that it needs”, suggesting he as prime minister would aim to undertake an overhaul of the health service.

He said Simon Stevens, the NHS chief executive, had once helped him get elected president of the Oxford Union as a student, and together they would “sort things out”.

In remarks that may alarm those opposed to another reorganisation of the NHS, Johnson said: “It needs more money but where you are absolutely right is that it needs reform.”

Jonathan Ashworth, the shadow health secretary, said the comments were “alarming but unsurprising given the hard-right agenda Johnson has been putting forward”.

“His tax plans will benefit the richest, he’s the biggest defender of the bankers who crashed the economy, and he’s been buddying up with Trump to sell off our NHS to US corporations,” he said. “His comments to Tory party members about his plans for the NHS need to be clarified immediately.”