Brexit talks between the Government and Labour will “peter out” within days, Sir Graham Brady believes.
The chairman of the 1922 Committee of Tory backbenchers also expects Prime Minister Theresa May to set out her timetable for departure at a meeting with him on Wednesday.
Speaking to the BBC’s Week In Westminster programme, Sir Graham, the Tory MP for Altrincham, said he would be bringing forward his own amendment on the Irish backstop to try and get a deal past MPs.
This is, in part, because he believes last-ditch talks between the Government and Labour to try and save Mrs May’s Brexit deal are about to break down.
“I find it very hard to see how that route can lead to any sensible resolution,” Sir Graham said.
“If the customs union is agreed without a second referendum then half the Labour Party won’t vote for whatever comes through regardless, and if a customs union is agreed then most of the Conservative Party isn’t going to support it.
“So, I can’t see that is a very productive route to follow, and I may be wrong, but I suspect it will peter out in the next few days without having come to any significant conclusion.”
Having ruled out cross-party talks as a potential solution to the deadlock, Sir Graham also suggested Mrs May’s deal will be “defeated by a large margin again” if she brings it back unamended, which is why he is lobbying for changes on the Irish backstop as a plan C.
He intends to bring forward an amendment stating the backstop would “stay in the text” but “obviously could never be used” – despite previous EU objections to anything that would destroy what negotiators term an “insurance policy”.
With Brexit options being rapidly whittled down, Theresa May had already offered up her premiership as the price for MPs backing her deal.
But even this has not been enough, and the clamour for her to go sooner reached fever pitch after calamitous council election results where the Tories lost nearly 1,300 councillors.
Earlier this week, Mrs May rebuffed demands to set out a timetable for her departure from Number 10 amid growing pressure from Tory MPs to make way for a new leader.
She was given another grace period by Sir Graham, who said he understood Mrs May’s “reticence” around setting out specifics on when she would go because it could scupper the chances for her deal.
However, the 1922 Committee chairman appears to have set his own deadline for a response.
He said: “I think that’s a natural concern and one can understand it, but it’s also the case the 1922 executive has asked her to give that clarity. She has offered to come and meet the executive, which we’ve accepted.
“It would be strange for that not to result in a clear understanding at the end of the meeting.
“We have asked the question and she is coming, I assume, to answer it.”
Sir Graham also did not rule himself out of what is becoming a crowded leadership race to replace Mrs May, but said “it would take an awful lot of people to persuade me”.
At Prime Minister’s Questions, Brexit-backing Tory MP Andrea Jenkyns told Mrs May she had “failed” in EU withdrawal negotiations and forfeited the trust of the public.
“The public no longer trust her to run Brexit negotiations,” she said.
“Isn’t it time to step aside and let someone else lead our country, our party and the Brexit negotiations?”
Mrs May retorted: “This is not an issue about me and it’s not an issue about her.
“If it were an issue about me and the way I vote, we would already have left the European Union.”
Downing Street made clear the Prime Minister was not ready to go beyond her earlier promise to the 1922 Committee to quit as Tory leader when the first phase of Brexit negotiations – dealing with the divorce terms – is complete.
“The PM made a very generous and bold offer to the 1922 Committee a few weeks ago that she would see through phase one of the Brexit process and she would leave and open up for new leadership for phase two,” a Downing Street source said.