Theresa May is under growing pressure to quit after a backlash over her last-ditch effort to get a Brexi deal through.
The Prime Minister will meet Sir Graham Brady, the representative of Tory backbench MPs, on Friday, for a meeting which could seal her fate.
The Prime Minister has previously agreed to set out the timetable for the contest to replace her after a crunch vote on her Brexit deal, widely expected on June 7.
That deadline appears to have been brought forward with the announcement she will meet Sir Graham, chairman of the backbench 1922 Committee, the day after a set of European elections which are expected to be disastrous for the Conservatives.
Sir Graham told reporters: "I will be meeting with the Prime Minister on Friday following her campaigning in the European elections tomorrow and following that meeting I will be consulting with the 1922 executive."
He said the executive discussed "all sorts of things" in the meeting.
The 1922 Committee's executive had been expected to consider a rule change to allow another attempt to force Mrs May out.
Following the failed bid to oust her in 2018, under the existing rules Mrs May would be safe from another confidence motion until December.
One Tory MP described the outcome of the 1922 Committee meeting as "the can kicked down (the road) until Friday".
In a sign of unrest at the highest levels of the Tory party, a series of Cabinet ministers asked for meetings with Mrs May to raise their concerns about the Withdrawal Agreement Bill (WAB) which would put the Prime Minister's Brexit plan into law.
Downing Street sources said it was possible that the PM could meet Foreign Secretary Jeremy Hunt on Thursday, but there was no confirmation that an audience would be granted for other ministers with reservations about the plan.
Home Secretary Sajid Javid has asked for a meeting to discuss his concerns about the prospect of a second referendum after May revealed she would grant MPs a vote on whether the Brexit deal should be put to the public.
Scottish Secretary David Mundell also has particular concerns because he fears the prospect of another referendum could be "exploited" by the SNP to call for a fresh independence vote.
READ MORE: David Mundell set for urgent meeting with Theresa May
In a visible sign that May's authority is slipping away, Brexit-supporting colleagues in the so-called “pizza club” were absent for the start of Prime Minister's Questions, with Cabinet ministers including Commons Leader Andrea Leadsom only appearing once the session was well under way.
In the Commons, May appeared to acknowledge that her premiership was drawing to a close, having already said she will set out a timetable for her departure after the crunch vote on her WAB.
"In time, another prime minister will be standing at this despatch box," she told MPs.
"But while I am here, I have a duty to be clear with the House about the facts.
"If we are going to deliver Brexit in this Parliament, we are going to have to pass a Withdrawal Agreement Bill.
"And we will not do so without holding votes on the issues that have divided us the most – that includes votes on customs arrangements and on a second referendum."
READ MORE: Prime Minister's 'straw poll' creates social media storm
The 1922 Committee's executive was asked to consider a rule change to allow May to face another attempt to force her out.
Following the failed bid to oust her in 2018, under the existing rules May would be safe from another confidence motion until December.
European Research Group chairman suggested it would be "more dignified and more elegant" if May followed the constitutional convention of quitting because she could not command a Commons majority.
In the Commons, as May defended her deal in the face of hostility from all sides, arch-Brexiteer Rees-Mogg asked "is she going through the motions or does she really believe in it?"
May replied: "I don't think I would have been standing here at the despatch box and be in receipt of some of the comments that I've been in receipt of, from colleagues on my own side and across the House, if I didn't believe in what I was doing."
READ MORE: Theresa May claims a vote for the SNP is a vote to 'betray democracy'
The WAB would be published on Friday and May said backing it would help get the UK out of 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.
But Tories expressed scepticism about whether May would be able to take the Bill to the Commons.
Tory MP Mark Francois said: "If I were a betting man, I bet £50 for Help for Heroes that the second reading of the WAB will never, ever happen and I invite another colleague, whoever it may be, to take my bet."
The SNP's Westminster leader, Ian Blackford, branded May’s new Brexit deal a "fantasy".
He asked: "Her customs union compromise already dismissed by the EU, isn't this new deal just a fantasy?"
May replied: "There is a difference of opinion in this House on the future customs arrangement with the EU, that's why it's important that this House actually comes to a decision on that issue.
"Allowing the second reading of the Withdrawal Agreement Bill will enable this House to come to a decision on that issue.
"It will also enable the House to come to a decision on a second referendum, which I continue to believe would not be the right route for this country to go down, we should deliver on the first referendum before suggesting anything about a second."
Blackford argued May's "time is up".
He said: "My goodness, talk about ignoring reality. Prime Minister, look at the benches behind you. The Prime Minister is fooling no-one but herself and the truth is that the people of Scotland don't want her deal.
"Her own party doesn't want her deal and now even the pro-Brexit Labour front bench won't support her deal, her time is up. Tomorrow, people in Scotland have a choice, to send a message, to send pro-European outward looking SNP MEPs to Brussels to stop Brexit.
"Prime Minister, what party does she think the people of Scotland will choose?"
May replied: "There is only one party in Scotland guaranteeing no more referendums and that's the Conservative Party."
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