The Prime Minister sounded the death knell on her premiership by telling Tory MPs she would stand down for the next phase of negotiations with Brussels.

Mrs May did not name a date for her departure from 10 Downing Street, but her announcement sets the stage for a likely Conservative leadership election within the coming weeks or months.

A steady stream of Eurosceptics have signalled they will now support the deal, with Boris Johnson the most prominent to perform a U-turn.

Prime Minister Theresa May has pledged to leave Downing Street if her Brexit deal is passed. Picture: Jonathan Brady - WPA Pool/Getty Images

Theresa May vows to quit as MPs vote no to Brexit options

The former foreign secretary, who once likened the deal to a “suicide vest” around the British constitution, told the Daily Telegraph he was “very, very sorry” to have changed his mind.

But he said “in the end, the thing I fought for may never happen” because unless Mrs May’s deal is passed, “I genuinely think the House of Commons is going to steal Brexit”.

His change of position was revealed at a meeting of the European Research Group (ERG) of pro-Brexit Conservatives shortly after Mrs May had made her own announcement at the Tory 1922 Committee.

Mrs May told her MPs: “I have heard very clearly the mood of the parliamentary party. I know there is a desire for a new approach - and new leadership - in the second phase of the Brexit negotiations - and I won’t stand in the way of that.”

But Mrs May’s sacrifice in the effort to secure the 75 votes needed to overturn the 149-vote defeat on her deal may prove to be in vain, with resistance among sections of the ERG - and the Democratic Unionist Party - remaining strong.

A source at the ERG meeting said: “There is no way enough votes are coming out of that room to put the Withdrawal Agreement through.”

Veteran Eurosceptic Sir Bill Cash told the Press Association the remaining rebels were a “Praetorian Guard for the vote of the British people” in the referendum.

“The reality is that, by every analysis, there are enough votes for us to carry our fight for the British people and for the democracy expressed in the referendum and the Act of Parliament that has been passed,” he said.

“It’s my understanding that the DUP are firm, it’s my understanding that there are enough votes in the Conservative Party even if there are some defections within the ERG ranks.”

DUP leader Arlene Foster said that the Northern Irish party “cannot sign up” to the deal because of its controversial “backstop” provisions designed to prevent a hard border.

The unionist party fears the measures will place a trade barrier in the Irish Sea, potentially seeing divergence between the rules in Northern Ireland and the rest of the UK.

Mrs Foster pinned the blame on the Mrs May, telling Sky News: “We are in a situation where we cannot sign up to the Withdrawal Agreement and it’s all because the Prime Minister decided to go for that backstop way back in December 2017.”

If Mrs May does risk bringing her deal back for a third Commons vote - after defeats by margins of 230 and 149 - it could take place on Friday, originally the day the UK was due to leave the European Union.

Meanwhile, none of the alternatives to Mrs May’s deal considered by MPs secured a majority.

Proposals for a second referendum on any Brexit deal won 268 votes and a customs union plan won 264, but both were defeated, by 27 and eight votes respectively.

A call for withdrawal without a deal was emphatically rejected by 400 votes to 160.

A further round of voting is expected to take place on Monday - as long as Mrs May’s deal has not been passed.

Brexit: Theresa May warned promise to stand down won’t win over Tory Eurosceptics