Theresa May is fighting to keep her Brexit deal alive to prolong her premiership as her grip on power weakens.
The Prime Minister will set out the timetable for her departure in early June after a crucial Commons vote on the agreement she thrashed out with the European Union, with defeat likely to hasten her exit from Number 10.
Mrs May’s chances of receiving Labour support for the Withdrawal Agreement Bill (WAB) appear to be fading, with Jeremy Corbyn’s party frustrated at the lack of progress in cross-party talks and the prospect of a new prime minister tearing up any compromise.
In a sign the negotiations are foundering, Mr Corbyn said he found it hard to deal with a Government in “disarray” and warned “the time limit is very soon”.
But Number 10 insisted the talks process, which began in early April, remained alive.
There were meetings between officials on Thursday and the prospect of the talks collapsing was “not how I see it”, a senior source said.
The Prime Minister will meet the chairman of the Tory backbench 1922 Committee Sir Graham Brady at the start of June to agree to the details of the leadership contest to succeed her.
The move follows a lengthy meeting on Thursday between Mrs May and the 18-strong 1922 executive during which she again came under pressure to name her exit date from Downing Street.
Even as the summit was taking place in Westminster, former foreign secretary Boris Johnson galvanised the race to succeed her, confirming he would be a candidate.
Mrs May and Sir Graham’s next meeting will come after the WAB has received a second reading vote in the Commons in the week beginning June 3.
Downing Street insiders indicated that if the Bill cleared its first Commons hurdle, Mrs May would seek to persuade the 1922 Committee to allow her to remain in office and secure Brexit, letting her leave having completed the main goal of her administration.
Mrs May wants the legislation to complete its progress by the time Parliament rises for its summer break, which is usually near the end of July.
“If the WAB goes through, she could say ‘this is my path for getting the Bill through Parliament, obviously it is something that is important to the ’22 to see Brexit delivered, and I want to see that through’ and then she is out after phase one,” a source said.
But if the WAB was defeated, she would face intense pressure to quit immediately.
The source said “she would have to say ‘this is how I envisage the timetable for a leadership election happening’ and there would have to be some sort of agreement about that”.
Sir Graham said the meeting with the Prime Minister on Thursday was a “very frank discussion”.
Mr Johnson will not be alone in seeking to replace the Prime Minister, with a crowded field of potential challengers already jostling for position.
International Development Secretary Rory Stewart wants the job and he has said “at least half-a-dozen” Cabinet colleagues also have leadership ambitions.