Outgoing PM says her successor must find solution that can win support of a majority of MPs

Theresa May has warned the two men vying to replace her against trying to bypass parliament, insisting they must find a solution to the Brexit deadlock that can win the support of a majority of MPs.

Boris Johnson has pledged to take Britain out of the EU on 31 October, “do or die”, and even declined to rule out proroguing parliament to override the objections of MPs.

But when asked about that suggestion, the prime minister said: “What I hope and expect is that my successor will be able to put before parliament proposals that will enable us to deliver on the vote of the British people in a way that will be good for the United Kingdom.”

Pressed on whether she herself would back whatever plan the next prime minister brings before the House of Commons, she said: “What you are saying to me is: ‘Will you now say that whatever happens in the future you’re going to agree with it?’

“Look, I think it’s important for us to deliver Brexit in a way that is good for British people. It will be up to my successor to take this forward, to find the majority in parliament that I was not able to find on this issue and to deliver the decision of the British people in 2016.”

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

It is highly unlikely there would be a majority for a no-deal Brexit, with several Conservative MPs, including Ken Clarke, Phillip Lee and Dominic Grieve, committed publicly to voting against a Tory government in a motion of no confidence, if that were the only way of preventing it.

Asked whether she could understand their motivations, the prime minister said: “This is an issue on which people feel strongly.”

Profile Jeremy Hunt's Tory leadership campaign Show Hide Personal style His style is notably technocratic, with few rhetorical flourishes and an emphasis on his consensual approach and long record as a minister, notably during more than five years as health secretary, a traditional graveyard of ministerial careers. Hunt’s attempts to talk up a backstory as an 'underestimated' entrepreneur can fall flat given he is also the son of an admiral and was head boy at Charterhouse. Overall, Hunt’s approach can seem uninspiring and hard to pin down in terms of core beliefs, hence the 'Theresa in trousers' nickname among some Tory MPs. Hunt has made headlines by promising to repeal the ban on fox hunting, while always facing scrutiny on his views on the availability of abortion. His campaign team have decided to take the fight directly to rival Boris Johnson though, with Hunt taking part in a Twitter Q&A session as a direct response to Johnson's refusal to appear on a Sky TV head-to-head debate. The hashtag: #BoJoNoShow. Brexit He says a new deal with the EU is possible by 31 October and he would send a cross-party negotiating team to Brussels, including members of the DUP. He would countenance leaving the EU without a deal but is notably more wary than rival Boris Johnson. Taxation Has been fairly silent on this, beyond a proposal to cut corporation tax from 19% to 12.5%, which according to the IFS would cost an estimated £13bn a year. Even at 19%, the UK rate is well below European and global averages. Public spending Before the campaign began he called for a doubling of defence spending, but he has since pulled back slightly, saying only that it should increase. He has argued that cuts to social care budgets had gone too far. Climate and environment Hunt backs the 2050 target for zero net carbon emissions and has called for 'sensible tax incentives' to encourage green initiatives, but very little beyond this. Foreign policy A likely strength for him, as he has been seen as a solid foreign secretary, an impression burnished by taking over from the chaotic Johnson. This has been a key part of his pitch. Peter Walker Political correspondent Photograph: Luke Dray/Getty Images Europe

But she added: “As far as I’m concerned, I believe there should be a Conservative government in the UK, because a Conservative government is better for the people of the UK.”

The prime minister was speaking to journalists en route to the G20 summit in Osaka – her final major international meeting before she leaves 10 Downing Street next month.

She resisted expressing a preference between Johnson and the foreign secretary, Jeremy Hunt.

But she repeatedly used the formula that whatever happens next in the Brexit saga must be “good for the United Kingdom”.

That would appear to rule out a no-deal Brexit, which she has warned in the past would be damaging – and declined to pursue earlier this year, when her own deal was rejected.

The race to succeed the prime minister has been dominated by the risks of a no-deal Brexit – with Johnson backed by many of the “Spartans”, who are relaxed about the prospect, which they regard as a way of escaping the controversial Irish backstop.

Both Johnson and Hunt have insisted their first course of action would be to seek changes to the backstop, with Johnson also suggesting he would “disaggregate” the withdrawal agreement, and withhold the £39bn financial settlement until after Brexit.

But May appeared to cast doubt on the likelihood of those strategies being successful, saying: “The EU has made its position clear. We negotiated a good deal with the EU.”

The prime minister was left with little choice but to resign, after the withdrawal agreement her government painstakingly negotiated with the EU27 was rejected three times by parliament, and talks with Labour failed to yield a way through the deadlock.

Asked whether she would do anything differently if she had her chance again, she said: “I did what I believed to be right in the interests of the country. Sadly, when it came to it on three occasions, I was not able to achieve a majority in the House of Commons for that decision. I think it’s right that somebody else will now take up that mantle and lead the country forward.”

May said she intended to stay on as the MP for Maidenhead after stepping aside and did not rule out standing as a candidate in the next general election.