Brexiteer Nigel Evans told The Sun: “She has U-turned on absolutely everything. We cannot put up with this any longer.

“I will be asking my colleagues tomorrow to agree to a rule change so we can hold an immediate confidence vote if Theresa is not prepared to stand down now.”

Mrs May had said she was giving a “bold new offer” to MPs but former Tory leader Iain Duncan Smith said: "There's nothing new or bold about this bad buffet of non-Brexit options.

"At a time when people are deserting the main parties this is the PM's response, to do all she can to defy the result of the referendum.”

Nigel Dodds, the DUP Westminster leader, said his party would examine the details of the Bill when it is published but “the fatal flaws of the draft treaty remain”.

He said that because the Bill still contains provision for the Northern Ireland backstop it remains a “bad deal” and the best way to get it through Parliament was to find alternative arrangements to the backstop.

Mrs May had been forced to water down plans to offer Tory MPs a free vote on a second referendum and a permanent customs union after Chris Grayling and Andrea Leadsom effectively threatened to resign during a “very heated” Cabinet meeting on Tuesday morning.

She said: "If MPs vote against the second reading of this Bill they are voting to stop Brexit.

"If they do so the consequences could hardly be greater - reject this deal and leaving the EU with a negotiated deal any time soon will be dead in the water and what would we do then?

"... If not no-deal then it would have to be a general election or a second referendum that could lead to revocation and no Brexit at all."

The former Cabinet minister Owen Paterson described the plan as “a direct insult” to the 17.4 million people who voted Leave in the 2016 EU referendum.

The Conservative MEP David Bannerman described the offer as “a total sellout” and said she must “go immediately”.

Watch Farage v Cable: The Brexit Debate live on The Telegraph at 9am on Wednesday