Eurosceptics have told Theresa May that defeat on her Brexit deal looks certain without more concessions from Brussels, even if she offers to quit in exchange for them voting to get it over the line.

The prime minister’s position is looking increasingly precarious, as cabinet ministers have floated the idea of forcing her to name a date for her departure if this could persuade hardline Eurosceptics to back her deal.

Some leave supporters may be tempted to go for this option to allow a Brexiter such as Boris Johnson, Michael Gove or Dominic Raab to take over and have a go at negotiating the second phase – or the future relationship with the EU.

However, the idea of voting for May’s deal in return for her exit was outright rejected by other Brexit supporters, with David Davis, a former Brexit secretary, saying it “will not get the vote through”.

“You can change the leader but you can’t change the numbers,” Davis told the BBC’s The Andrew Marr Show. “We have got to focus on the issue here … Nothing else will work.”

Some of the most hardline leave backers are implacably opposed to the deal unless the attorney general, Geoffrey Cox, secures a legally binding way out of the Irish backstop, which as it stands could keep the UK in a permanent customs union with the EU.

Writing for the Sunday Telegraph, Steve Baker, a leading figure in the European Research Group, and Nigel Dodds, the leader of the Democratic Unionist party, described defeat for the deal as “inevitable” and predicted a “three-figure majority” against the deal – a similar position to last time.

“An unchanged withdrawal agreement will be defeated firmly by a sizeable proportion of Conservatives and the DUP if it is again presented to the Commons,” they wrote. “If with the DUP just half of previous Conservative opponents vote against the deal, a three-figure majority would be expected.”

Brexit supporters were this weekend gearing up to blame Brussels for failing to offer enough concessions to get the deal over the line.

Iain Duncan Smith, the former Tory leader and cabinet minister, wrote in the Mail on Sunday: “If reports are to be believed, the EU has acted in bad faith and rejected [Cox’s] proposals for a simple but legally binding guarantee that the backstop, the agreement which prevents a hard border in Ireland, would not lock Britain in for ever.

“And it is clear that unless there is such a guarantee, the backstop – which puts us in ‘temporary’ alignment with EU trade rules – is indeed a trap from which the UK might never escape.”

Raab, a former Brexit secretary and leading contender for the leadership, told Sky’s Sophy Ridge on Sunday: “We’ve seen total intransigence from the EU.”

Quick guide Tory leadership contenders Show Hide Jeremy Hunt 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 – one that is more catchy than accurate (since May herself often wears trousers). In the final round of MP voting Hunt edged out Michael Gove, 77 votes to 75. Boris Johnson Johnson’s progress to Downing Street appeared unstoppable even before an overwhelming victory in the first round of voting among MPs. Most of his colleagues believe it is now all but inevitable that he will be Britain’s next prime minister. His well-disciplined campaign team will continue with their strategy of subjecting him to minimal media exposure, though once the field is narrowed down to two, the final pair will appear in more than a dozen head-to-head hustings for Tory members. The team’s main aim is simply to keep heads down and avoid Johnson creating headlines for the wrong reasons. It may not have worked. Johnson came first in the final round of MP voting with 160 votes.



However, supporters of May have not entirely given up on getting the deal through parliament. Cabinet ministers planning to back the prime minister’s agreement hit the airwaves on Sunday to warn colleagues of the consequences of refusing to back her on Tuesday.

Jeremy Hunt, the foreign secretary, said the consequences of Conservative MPs voting down the deal would be electorally “devastating” for the party, which would be blamed for failing to deliver Brexit. He called for “realism” among Eurosceptics, wsaying failure to back the deal would lead to an extension, and then possibly a second referendum.

Adding to the pressure on MPs, Philip Hammond, the chancellor, is expected in his spring statement on Wednesday to offer Conservative MPs a £20bn pot of money to “end austerity” if the prime minister’s deal passes.

Brexit secretary met Labour MPs championing second referendum plan Read more

If May’s deal fails to pass, she has committed to holding votes in parliament on whether to rule out a no-deal Brexit and whether to extend article 50, both of which MPs are likely to support.

Campaigners for a second referendum then hope that they could gain momentum while the UK remains in limbo and the prospect of a no-deal Brexit becomes more real.

However, May’s team would push for more talks with Brussels and try to hold a third meaningful vote on her Brexit deal. She could be forced to try to strike an agreement with the opposition on a customs union with the EU, a move that would infuriate the Eurosceptics and worsen Conservative divisions.

Downing Street insiders are privately concerned that May will not be able to hold on to power for long enough to get to the point of a third meaningful vote, as she could be forced by colleagues to resign and allow a replacement leader to conduct a “Brexit reset”.