FORMER education secretary Justine Greening said other senior Conservatives quietly back a second Brexit referendum.
Greening, who quit Theresa May's Cabinet in January, said Parliament is "gridlocked" over Brexit and the public should be given another vote that includes the option to remain in the European Union.
The Putney MP told BBC Radio 4's Today she would campaign for Remain in any new vote. Asked if any other senior Tories backed a second referendum, she said: "Yes I believe so."
Discussing the Prime Minister's Chequers plan for Brexit she said: "I don't think it can work. I think it was a genuine clever attempt at a compromise that could work.
"But in practice having looked through the detail now it just won't and I cannot see how, going forward, the common rulebook will be workable in practice.
"What we need is a clear route forward that settles this European question once and for all."
Tory Brexiteer Sir Bernard Jenkin suggested May's Chequers plan was "dead".
He told Today: "I'm afraid it is neither beloved by Remainers or Leavers.
"It's also quite likely to be either rejected by the EU or more demands will be made upon it so it will be even less acceptable."
He described Greening's call for a second referendum as "a little ill-thought out", saying: "If we wanted to extend the uncertainty for another long period this is one way of doing it."
Business Secretary Greg Clark warned Tory would-be rebels against supporting amendments tabled by arch-Brexiteers, saying they risked harming the country's ability to trade after leaving the European Union.
He told Today: "The amendments are to a Bill that is designed to prepare for the world after Brexit, to be able to establish new customs regime that will be necessary.
"So I would hope and expect that those of my colleagues that want to get on with Brexit would recognise that this Bill is essential."
Asked about the chances of success for May's strategy, Clark told Today: "This is a White Paper that is now the basis of our negotiation. What I hope is that the EU should now respond positively to that.
"If, as I expect, that happens and we have a comprehensive deal that can be put before Parliament - and there had been a commitment to have a meaningful vote - what comes with that is the certainty for working people right across the country that will be able to invest with confidence, will be able to create new jobs, that implementation period will be available.
"All of that hinges on that being agreed this autumn and, I think, when it comes to Parliament, I hope and expect that it will be persuasive that what is on offer will be good for the UK and good for every part of the UK."
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