Theresa May has been warned 40 pro-EU Tory MPs would vote against any Canada-plus type deal favoured by hardline Brexiteers.
Former home secretary Amber Rudd admitted there was now an “impasse” between two factions of the party and that a second referendum might be the only way to break the deadlock.
On the Brexiteer side, David Davis last week told HuffPost UK up to 40 Tory MPs are prepared to vote against the prime minister’s Chequers plan.
It comes as Jeremy Corbyn is due to meet EU’s chief negotiator Michel Barnier in Brussels today.
The Labour leader has said his party would vote against the Chequer’s plan “as it stands. The Opposition would also not back a Canada-style agreement.
But he offered the prime minister a way out by revealing he would back a “sensible deal”, saying he would support an outcome that features a customs union and no hard border on the island of Ireland.
Speaking to ITV’s Peston programme on Wednesday evening, Rudd said she would prefer a second referendum to a no deal Brexit.
She suggested one outcome that could survive a vote in the Commons was a “Norway style EEA deal”.
Asked if she would back a Canada-style deal, she said: “No. I think there are a number of people, in fact I’ve talked to a few colleagues and I reckon there are conservatively about 40 of us who would not support a Canada type deal.
“But to be frank there are so many reasons a Canada type deal doesn’t work, starting with the Irish border, going on to manufacturing, that I think we can make those arguments.
“But that just reinforces the point that there is an impasse, if the two wings of our party face up to the fact that we have these elements that differentiate us, but the rebel group need to think again because I think we’ve only got one shot at a negotiated settlement.”