Speaking to BBC Newsnight, Ms Dorries said: “I can feel a growing consensus among a number of MPs — faced with these Europhile kamikaze MPs, who really don’t care about their careers going up in flames, who want to overturn parliamentary tradition in order to stop Brexit — I think many people are now realizing that we would support this deal to get it over the line.

“Because every day here is a dangerous day at the moment. We may have to see that this is a deal, we will have to swallow our pride, swallow what we would prefer, and vote for it.”

She later clarified that she would only support the deal if Mrs May secured changes to the backstop, as set out in her speech to MPs on Monday afternoon.

It follows reports that Amber Rudd, the Work and Pensions Secretary, has warned Downing Street that up to 40 ministers could quit so they can support backbench plans to take no deal “off the table”.

At least four other Cabinet ministers share her concerns and are understood to have issued similarly stark warnings to the Prime Minister as part of a push for a free vote on the issue next week.

However, the former Tory leader Iain Duncan Smith has this morning urged Mrs May not to give into their demands, suggesting that Ms Rudd and other should resign if they disagreed with her.

"The Government has to have a position on something as fundamental as what their plan is for the future,” he added.

"The Prime Minister was very clear yesterday and there is collective responsibility in Cabinet and among ministers - they have agreed there will be no extension of Article 50, there will be no revocation of Article 50 and no customs union."