Former prime minister Tony Blair has suggested Theresa May should pull next Tuesday's vote on her Brexit plan rather than go down to a heavy defeat.
Mr Blair said that instead of trying to force her plan through against opposition from both Brexiteers and Remainers, the PM should play the role of "facilitator" to find a compromise which can command a majority in the Commons.
But he predicted that none of the Brexit options on offer would prove capable of attracting majority support from MPs, and the question would then have to be put back to the public in a second referendum.
On the ballot paper for a re-run poll should be the choice of remaining in the EU, possibly with concessions on immigration and free movement if these could be obtained from Brussels, and the kind of hard Brexit favoured by those he termed "proper Brexiteers".
Speaking at a Westminster lunch, the former Labour leader said Mrs May faced the prospect of "hitting a brick wall at speed" in the December 11 "meaningful vote".
Asked if she should call the vote off, Mr Blair said: "Personally, I don't see what the point is in going down to a huge defeat.
"But I think that's a second-order question.
"The real issue is, is she prepared to work to see what is a compromise that has parliamentary approval?
"My belief is that when that process goes through, she will find that there isn't one.
"And if there isn't one, that's when my solution becomes more acceptable."
Mr Blair said the Prime Minister would be better to recognise the reality of her situation than "just going ahead".
"When you look at what Theresa May should do, if she can't get this thing through, she's got to be the facilitator of finding the thing that works," he said.
"And it is better to be in that position because that's the reality of where she is, than just kind of going ahead knowing you are going to hit that brick wall at speed."
Although a second referendum with Remain on the ballot paper seemed improbable, it provides the only solution if all Brexit options prove impossible in a deeply-divided Parliament, he said.
"I'm 100% at a personal level sympathetic to her," said Mr Blair.
"But honestly, this is the moment to realise you are going to have to work out whether it's possible to reach a consensus amongst the MPs.
"And if it isn't, you exclude the impossible and go back to the improbable, because that's all that will work."
Mr Blair said that the nation was "united" in believing that the UK should either do Brexit or not do it, but would not accept a result which is "half in and half out".
By making the "strategic error" of trying to balance the need to deliver on the referendum result with the imperative to limit the economic damage of EU withdrawal, Mrs May had "tried to square a circle that can't be squared".
Her deal "doesn't honour the Brexit vote and doesn't satisfy Remainers either", and if it was pushed through, it would be regarded as a "betrayal" by many of those who voted Leave in 2016, he said.
Turning one of his own slogans on its head, Mr Blair said: "This time, there's no acceptable third way."
With Mrs May's Government "at bay and in disarray", Mr Blair said he was "heartily thankful" that MPs had reasserted the power of Parliament to show leadership on the way forward, with Labour and Tory MPs showing a readiness to co-operate across party lines.
"There is a cohesion and willingness on the part of MPs to provide the ordered set of choices which the Government is unable to grasp," he said.
"Where it ends is anyone's guess.
"My guess, and I may be 100% wrong, is that when all the options are voted upon, Parliament will come to the view that none can truly be said to reflect the majority will of the people, and it's back to them therefore that we must go for resolution."
Mr Blair rejected Mrs May's position that her deal must be approved in order to draw a line under Brexit divisions, warning that it would fail to settle arguments which would then continue beyond March 29 2019.
And he questioned Brexiteers' warnings of civil disorder if a fresh referendum was called, saying: "It would be a curious thing to go and riot on the streets because you are being asked your opinion."