“If it is not killed off it will only grow and grow. Appeasement only emboldens them,” one MP said.
Mrs May is set for a crunch battle with Tory Remainers on Wednesday as part of a crucial round of voting on the EU Withdrawal Bill.
It comes after they rejected her attempts to agree a compromise over demands that MPs get a greater say over Brexit.
A ceasefire was declared briefly last week after Mrs May agreed to listen to their concerns. But after hours of negotiations the Remainers attacked a compromise amendment Mrs May had believed all MPs could support.
Theresa May is ‘steadfast’ in her belief that Parliament cannot be allowed to block Brexit
She’s taken back control. Now the rebellion has got to be put down
No 10 sources said the Prime Minister was “absolutely holding steadfast” to a series of principles, including that Parliament could not be allowed to overturn the will of the people shown in the EU referendum.
They said they would be “working hard” until Wednesday to get MPs on board. No 10 believes its approach has peeled off some of the rebels.
It also hopes that some Labour MPs will vote with the Government. But some Remainers hold out hope that a Government defeat could help them overturn the referendum result.
Pro-Brexit Tory MPs said Mrs May could not show weakness in the face of threats from Remain MPs.
They warned if she did not defeat the rebels – leaving the country heading for a watered down Brexit – the consequences for her could be dire.
A leadership contest can be triggered if 48 MPs lodge a letter with the chairman of the backbench 1922 Committee.
One Tory MP said: “If the amendment had been what the rebels wanted in full last week, my letter would have been going in next week. And I know that other people’s letters would have been going in as well.
“She’s taken back control. Now the rebellion has got to be put down.”
Losing on Wednesday night could damage Mrs May’s leadership.
Behind the scenes, some Tory MPs are arguing that defeat would show that she cannot get key Brexit legislation though Parliament and that another general election is needed.
Before that, however, some believe that the Conservative Party would have to replace Mrs May, who backed Remain in the referendum, with a Brexit leader.
Wednesday will be a crunch moment for Remain MPs facing a tough choice over whether to push ahead with their demands while hurting their leader.
Last week Mrs May vowed not to accept “anything that prevents us from taking back control of our money, laws and borders”.
Tory MP Antoinette Sandbach said she and her colleagues were ‘not rebels’
On Wednesday she told MPs: “The Government’s hand in the negotiations cannot be tied by Parliament, but the Government must be accountable to Parliament.
Government determines policy and we then need parliamentary support to be able to implement that policy. “I cannot countenance Parliament being able to overturn the will of the British people.
Parliament gave the decision to the British people, the British people voted to leave the European Union and, as Prime Minister, I am determined to deliver that.”
Tory MP Andrew Bridgen said: “The Prime Minister is absolutely right to resist any demand to give Parliament a veto on the final deal as this would guarantee a poor deal from the EU.”
Tory MP Antoinette Sandbach, among those expected to vote against the Government, said at the weekend she and her colleagues were “not rebels”.
She said: “We are pragmatic Leavers. We don’t want to go off the edge of a cliff which would be a disaster for my constituents,” she said. But there was criticism of one of the group’s leaders – former attorney general Dominic Grieve – after it emerged he told MPs last year that he did not want to “fetter the Government’s hands in negotiations or indeed the Government’s right to walk away from the negotiations”.
Mr Grieve insisted a “contingency” had to be put in place in case negotiations collapsed. Conservatives have also highlighted 20 Labour MPs who they said “voted against taking back control this week” despite representing Leave areas.
1 of 10
They included Pat McFadden, the former shadow Europe minister.
The MPs expressed their support for a Norway-style deal which Labour leader Jeremy Corbyn said would leave the UK “taking rules from Brussels but having no role in making them”.
Meanwhile, Mrs May was facing another potential difficulty last night as Sinn Fein’s leader warned Brexit could not progress without agreement on the Irish border.
Sinn Fein wants Northern Ireland to remain part of the EU customs union after Brexit, even though Mrs May has ruled this out.
A deal has to be done on the border, one of the most vexed issues facing the negotiators in Brussels, by this autumn to meet the Brexit timetable.
A time-limited “backstop option” – which the EU interprets as Northern Ireland staying in the Customs Union – would be introduced.
Jeremy Corbyn said a Norway-style deal would leave the UK ‘taking rules from Brussels’
Q & A on the challenges ahead for the Government
What are Tory rebels demanding?
A “meaningful vote” to avoid a hard Brexit if there is no trade deal in place by the time the UK leaves the EU next March. Theresa May narrowly avoided defeat in 11th-hour talks after rebels accepted significant concessions from the government last Tuesday.
What happens next?
On Monday, peers will vote again on the so-called Hailsham amendment. It says that if by February 2019 – only weeks ahead of the exit date of March 29 – there is no deal, MPs will be empowered to direct the Government. The amendment won a majority of nearly 100 when peers voted on the measure last month and turnout this time is expected to be greater.
On Wednesday the amendment comes back to the House of Commons. Rebels maintain there is still no majority for a hard Brexit and they can defeat the Government. However, Brexiteers and a handful of Labour rebels think they can still win and have urged the PM not to make any more concessions. If May loses the crunch vote it could split the Conservatives.
What is the time line for negotiations?
The Brussels summit on June 28/29 will see EU leaders discuss Brexit progress and the Irish border issue, without the UK. EU chief negotiator Michel Barnier said negotiations must be complete by the EU summit on October 18/19 when a Brexit deal will be put to the member states.