After MPs again voted to reject the Prime Minister’s Brexit deal on Friday, Nicky Morgan said a cross-party coalition may be the only way to break the deadlock.
The Commons is due to hold a second round of indicative votes on Monday on alternatives to Mrs May’s plan amid warnings that Westminster is rapidly running out of time to resolve the crisis.
With the Prime Minister determined to bring back her deal for a fourth time, Mrs Morgan said if MPs were able to coalesce around one of the alternatives it may need a unity government to implement it.
“If the Government refused and Theresa May felt she could not implement what Parliament had identified as a way of leaving the EU, then I think we would have to think very hard about whether a cross-party coalition, group of people, whatever, could do that in order to make sure that the UK does leave the EU in an orderly fashion,” she told the BBC Radio 4 Today programme.
The former education secretary - touted as a possible “unity” prime minister - added: “It may well be that if you end up with a cross-party approach to finding a majority in the House of Commons it might be that you need a cross-party approach to implementing it.
“There have been periods in our history when we have had national unity governments or a coalition for a very specific issue.”
Her comments came after Labour deputy leader Tom Watson suggested the time had come for a national unity government.
In an interview with Prospect magazine, he said: “I prefer Labour governments and I hope we never get to a point where our economy or security is so in peril that we get a government of national unity.”
But he added: “If needs must, we have to then do what’s right.”
There appeared to be little enthusiasm for the prospect among those around Jeremy Corbyn. Shadow transport secretary Andy McDonald told Today: “I’m not sure that’s going to be the solution.”
Conservative Party chairman Brandon Lewis also rejected the idea, insisting that Mrs May’s deal was still the best way to deliver an orderly withdrawal from the EU.
“A national government is not the answer. It doesn’t change the parliamentary maths and the fact that when MPs have voted they have consistently failed to come to a conclusion,” he told Today.
Mr Lewis made clear the Government remained opposed to the option which came closest to a majority in the first round of votes on Wednesday - a proposal by veteran Tory Ken Clarke for a customs union.
“There would be a huge number of people around the country who would understandably take the view that doesn’t respect the (referendum) vote of 2016 and it goes against our party’s manifesto,” he said.
Meanwhile, the Prime Minister is under renewed pressure from the Brexiteer wing of the party after she said it was “almost certain” that there would have to be an extended delay to Brexit if her deal does not go through.
Following the defeat on Friday, she warned the Commons would not allow Britain to leave without a deal on April 12 - the new deadline set by the EU.
Any extension beyond that date would require Britain to take part in elections in May to the European Parliament.
According to The Sun, 170 Tory MPs have now written to the Prime Minister demanding the UK leaves within the next few months and insisting it cannot take part in the European elections.
The letter was said to have been signed by 10 members of the Cabinet - including Foreign Secretary Jeremy Hunt and Home Secretary Sajid Javid - and 20 other ministers.
Mr Lewis said: “I haven’t signed the letter. I do know about it. I haven’t seen the full text of the letter and I haven’t seen the signatures on it.
“My view is that we should be doing everything we can to leave the European Union in good order as quickly as we can. I think the deal is the right way to do that.
“We must do everything we can to ensure we do not fight the European elections. None of us wants to do that.”