In a stark warning, former Brexit minister Steve Baker said the Conservative Party faces a "catastrophic split" if Theresa May sticks to her Chequers plan for future relations with the EU.
TUC general secretary Frances O'Grady said: "Whether it's through a general election or a popular vote, Mrs May should take her deal on the terms of Brexit and put it back to the people".
Baker is the former chairman of the Eurosceptic body the European Research Group, which plans to publish its own proposals for Brexit ahead of the Conservative Party Conference. Unattributed comments included "everyone I know says she has to go", "she's a disaster" and "this can't go on", the BBC reported.
"So, we all need to just be cautious in what we do and what we say, and support Theresa May (and) invite her to change the policy".
Brexiteers have said as many as 80 of May's 315 lawmakers could vote against her so-called Chequers plan, leaving the fate of the government and the Brexit deal in the hands of the opposition Labour Party.
May's proposals, named for a country house where they were hashed out in July, call for free trade of goods with the European Union, with Britain accepting a "common rulebook" that would apply to those goods.
The controversial agreement, which set out a blueprint for the future relationship with the European Union following Brexit, has led to the resignation of then-Brexit Secretary David Davis and Johnson.More news: The Last Remnant Remastered announced; coming west on December 6
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"I disagree with her on one issue", Davis said.
Hopes of a deal breakthrough have helped sterling to rally almost 2.5 percent from Wednesday's lows below $1.28 and tighten five-year credit default swaps by more than a basis point from a near 1-1/2 year high hit this month. He has beforehand indicated that settlement would be foremost by mid-November to enable time for the foremost ratification procedures.The Brexit deal is to embody the so-known as divorce terms, as neatly as ushering in a 21-month transition duration.
Even a small rebellion inside May's party on a vote over a final deal could spell the end of her minority government and throw Britain's exit into chaos. "The truth is that we reconsidered", he added.
The comments came amid open warfare in the Tory ranks following former foreign secretary Boris Johnson's comparison of the Government's Brexit strategy to placing the United Kingdom in a "suicide vest" and handing Brussels the detonator. We have wrapped a suicide vest around the British constitution - and handed the detonator to Michel Barnier.
Andrea Jenkyns, who has submitted a letter of no confidence in May, told AFP the prime minister was "too dogmatic" to change course. Under Conservative rules, a leadership election is triggered if 15 percent of Conservative lawmakers demand a vote of no confidence.
A debate in Parliament has been triggered by a petition signed by nearly 200,000 people arguing that the Article 50 notice to leave the European Union should be withdrawn due to Brexit campaign Vote Leave's overspending.
May's government says its critics have failed to present a viable alternative to her Chequers proposal.