Speaking on Sky News, the Chairman of the Foreign Affairs Committee argued a parliamentary rejection of Theresa May's final Brexit deal with Brussels will most likely result in her Government being overthrown.
'I hope very much the government will look at that, because I think it provides a solution which would satisfy everybody, ' he said.
With not all rebels persuaded that May's plan can prevent an economic shock after Brexit, some say they will challenge her plans to leave the customs union again during votes on other bills, on trade and customs, which will be brought back to the house some time before July 24.
The issue was at the heart of a knife-edge vote on Tuesday, which saw more than a dozen MPs, including Nicky Morgan and Ed Vaizey, called into the prime minister's office to be given last-minute reassurances their concerns would be addressed.
May, who leads a minority government propped up by the small Northern Irish Democratic Unionist Party (DUP), conceded that "we need parliamentary support" to implement Brexit.
Labour split three ways as the Commons debated a Lords amendment to the EU (Withdrawal) Bill calling for EEA membership to remain on the negotiating table.
Jeremy Corbyn urged his MPs to abstain but 75 voted for and 15 against, while six quit their frontbench roles.
And former attorney general Dominic Grieve withdrew his own proposals spelling out precise terms under which MPs should be given a "meaningful vote" on the eventual deal - including the power to dictate what the UK Government should do if no acceptable agreement is reached by February 2019.
"I absolutely trust what the Prime Minister says to us", he told BBC Radio 4's PM programme. It was sealed at a private meeting between May and potential rebels. Part B said that if no deal with the European Union was reached by 30 November 2018, the government would have to come to parliament and explain exactly what would happen next.
"In all conscience, I can not support the Government's decision to oppose this amendment because doing so breaches such fundamental principles of human rights and Parliamentary sovereignty".
"The question is how do we take some sensible steps to anticipate that happening and try to make sure that there is a coherent process for dealing with it".
The Prime Minister appeared to have defused a potentially explosive row over the EU customs union on Monday night as Tory pro-Europe rebels Sir Oliver Letwin and Nicky Morgan and Brexiteers Jacob Rees-Mogg and Sir Bill Cash came together to table a separate compromise amendment backing "a customs arrangement" with the EU.
"We will wait and see the details of this concession and will hold ministers to account to ensure it lives up to the promises they have made to Parliament".
Ms Allen said: "No Tory MP, not a single one, is trying to stop Brexit".
"Time will tell as to whether this is just another attempt to buy off the rebels or a real attempt at consensus".
Senior Tory Nigel Evans added: 'Bracknell folk voted out by a greater margin than the United Kingdom - we all stood on a manifesto only a year ago to deliver brexit and that is what the people now expect.
After winning yesterday's ballot over changes to a future "meaningful vote" on a final agreement with Brussels in her European Union withdrawal bill, May's plans to end more than 40 years of membership in the bloc were still on track.