Theresa May is set to force her cabinet to keep open the option of a no-deal Brexit despite threats of ministerial resignations.

The Prime Minister is expected to whip her ministers against fresh cross-party plans to let MPs seize control of the parliamentary process for exiting the EU, HuffPost UK has been told.

May’s hard line came as Labour looked increasingly likely to back an amendment by Yvette Cooper, which will delay Brexit by nine months if no agreement can be reached by February 26.

Shadow Chancellor John McDonnell told BBC’s Newsnight that the party was minded to back Cooper’s plan, though possibly if it reduced the Brexit delay to three or six months rather than wait until the end of the year.

Although some minsters have threatened to quit rather than allow the UK to crash out of the EU without a deal, several now believe there are enough Tory backbenchers ready to kill the idea.

No cabinet minister pushed the idea of a ‘free vote’ in cabinet on Tuesday and Chief Whip Julian Smith warned all those present that collective responsibility applied to everyone.

A government source said they would be ‘very surprised’ if the PM allowed a free vote.

Ministers and MPs now expect to a three-line whip to be applied to every amendment that undermines the government’s position.

One cabinet minister told HuffPost UK that the PM was sticking to her line that she did not want any ‘indicative’ votes or to allow Parliament to seize from government the right to control Commons business.

Work and Pensions Secretary Amber Rudd has reportedly warned Downing Street that up to 40 ministers could quit rather than accept a no-deal outcome.

Solicitor General Robert Buckland even went public on Sky News to call for a free vote.

“The grim reality is that if we don’t sort this out within the next week, then things could go out of control, that parliament could start asserting its authority in the way that we have seen — and that means more chaos,” he said.

However, with the PM ruling out a free vote, it is likely ministers will rely on backbench colleagues to join with opposition parties to block no-deal and delay ‘Exit Day’, due on March 29.

Justice Secretary David Gauke is understood to have backed off his earlier threats to quit over the issue. Just a week before the PM has to bring a new Brexit statement before the Commons, backbenchers tabled a raft of amendments that eurosceptics warned could cause “mayhem” to the way parliament works.

At least eight amendments were tabled, with more expected in coming days, as MPs marshalled their forces to prevent what business chiefs warned on Tuesday would be a ‘cliff-edge’ Brexit.

Cooper’s plan, which was described by Shadow Business Secretary Rebecca Long-Bailey as ‘fantastic’, came as former Attorney General Dominic Grieve unveiled his own plan to force the government to guarantee time for votes on alternative Brexit plans.

Grieve’s amendment effectively forces the House of Commons to debate and vote on Brexit ‘Plan Bs’ on nearly every Tuesday for six weeks, on February 12 and 26, and March 5, 12, 19 and 26.

As business released new research on the dangers of a ‘cliff-edge’ exit in March, Labour backbenchers Rachel Reeves and Hilary Benn tabled their own, non-binding amendments to delay Brexit and to call for a series of ‘indicative’ votes respectively.

Tory Caroline Spelman and Labour MP Jack Dromey tabled a simpler option, urging MPs to say they ‘reject’ the UK leaving the EU without a deal. Further amendments, on a ‘Norway-plus’ Brexit or a second referendum, have yet to be tabled.

But amid signs that Brexiteers and the DUP were coming back on board for the PM’s plan, Tory MP Andrew Murrison re-tabled his own amendment to insist that the UK would never be trapped in a customs ‘backstop’ with Brussels. His amendment ‘insists on an expiry date to the backstop’.

Former cabinet minister Iain Duncan Smith warned on BBC Radio 4 that the “constitutional nonsense of allowing a backbench group to take over the business” proved that some MPs were “living in cloud cuckoo land”.

“If the Labour party agrees to support that they have to think carefully what would happen if they were in power and they did not have a massive majority. This opens the door to mayhem in the Commons.”

CBI boss Carolyn Fairbairn, one of several business chiefs to join a conference call with the PM on Tuesday, pointed to a new analysis of government figures which showed that every region of the UK would lose GDP in a no-deal Brexit.

“The message from business cannot be simpler: a March no-deal must be ruled out immediately. This is the only way to halt irreversible damage and restore business confidence.

“The best route to pulling back from the cliff edge is for politicians of all parties to start showing real flexibility.”