The party’s influential 1922 Committee executive met to discuss changing party rules to allow a vote of MPs to force May out of Downing Street.

But the Prime Minister reportedly refused to resign, fearing the consequences for Thursday’s vote in the European Parliament election, and the 1922 Committee did not put any proposed rule change to a vote.

She agreed to meet the 1922 chairman on Friday to discuss her position.

The Conservative party will now see an intense struggle for control, with at least six ministers in the running to replace May and former Brexit secretary Boris Johnson the favourite to take her place.

And the UK will vote on Thursday without knowing who will lead the country next week, or what their plan for Brexit is.

Just 24 hours after May outlined a “new Brexit deal” for Parliament to vote on in early June, it became increasingly clear there was little chance of her winning enough MPs’ support.

May faced Parliament on Wednesday for a two-hour session defending her "New Brexit Deal", but the government benches were sparsely populated and even former allies pleaded with her to rethink her plan and tactics.

Many were concerned the legislation would be a millstone around the neck of her successor.

The last straw for May’s colleagues was reported to be a line in her proposed Brexit legislation which set out the path to a second Brexit referendum, subject to a vote in Parliament.

Under party rules she was immune from a formal leadership challenge until December. She had already accepted that she would be gone before then, but has not set a firm timetable.

The 1922 Committee of Conservative MPs has the power to end her immunity.

It is 1043 days since May took the prime ministership in the wake of the Brexit referendum. She has to survive just one more week in the job to beat Gordon Brown and become the UK’s fifth, rather than fourth shortest-serving prime minister.

May told the Commons if it passed her Brexit legislation then the UK would leave the EU “by the end of July”.

“We can bring an end to the months - years - of increasingly bitter argument and division that have both polarised and paralysed our politics,” she said.

“Reject it and all we have before us is division and deadlock. We risk leaving with no deal, something this House is clearly against.

“We risk stopping Brexit altogether, something the British people would simply not tolerate. We risk creating further division at a time when we need to be acting together in the national interest.

“And we guarantee a future in which our politics become still more polarised and voters increasingly despair as they see us failing to do what they asked of us. None of us want to see that happen.”

But many Conservative MPs have already indicated they will reject her Brexit plan.

Brexiter Jacob Rees-Mogg dismissed it as “folderol”, which Commons Speaker John Bercow helpfully explained meant “a showy or useless item, or an unnecessary or inconsequential fuss”.

Labour leader Jeremy Corbyn said May had changed her rhetoric on Brexit but the deal was essentially the same one that Parliament has already rejected three times.

“The government is too weak, too divided to get the country out of the mess they have created,” he said.

“No matter what the Prime Minister offers it is clear that no compromise would survive the upcoming Tory leadership contest… No Labour MP can vote for a deal from a Prime Minister who has only days left in her job.”

Many Labour MPs indicated they would have supported the Brexit bill if it had explicitly guaranteed another Brexit referendum.