British Prime Minister Theresa May is clinging to power as she faces letters of no confidence and the shock exodus of four ministers in protest over her Brexit plans.

Leading Brexiteer Jacob Rees-Mogg became the latest minister to submit a letter of no confidence to Ms May on Friday morning (AEDT), increasing the chances of the Prime Minister facing a leadership spill.

The move came hours after Brexit Secretary Dominic Raab and Work and Pensions Secretary Esther McVey sensationally walked out of the government after cabinet agreed a draft European Union withdrawal agreement in a stormy five-hour meeting.

Two more junior ministers – Suella Braverman at the Brexit Department and Shailesh Vara at Northern Ireland – also quit along with two parliamentary aides.

In a letter to Sir Graham Brady, chairman of the backbench 1922 Committee, Mr Rees-Mogg said Ms May’s Brexit deal “has turned out to be worse than anticipated and fails to meet the promises given to the nation by the Prime Minister, either on her own account or on behalf of us all in the Conservative Party manifesto”.

His move is expected to be matched by other members of the European Research Group, which he chairs.

At least 14 Conservative MPs have openly admitted they have submitted such letters, although others could have done so secretly. Forty-eight are needed to trigger a challenge.

Mr Rees-Mogg told journalists the next Prime Minister should be someone who believed in Brexit.

The Labour Party said the government was “falling apart”.

Ms May’s Brexit deal came under a hail of criticism in the House of Commons, where only a handful of Tories spoke in favour of an agreement thrashed out in 19 months of intensive negotiations.

There was laughter from opposition benches when the PM said her deal would allow the UK to leave the EU “in a smooth and orderly way” on March 29.

Ms May insisted the deal was in the national interest and offered a future relationship with “a breadth and depth of co-operation beyond anything the EU has agreed with any other country”.

Ms May called a news conference at her Downing Street residence to underline her determination to stay the course.

Asked if she would contest any challenge to her position, she replied: “Am I going to see this through? Yes.”

Mr Rees-Mogg told Ms May the deal did not match up to her previous promises on quitting the customs union, maintaining the internal integrity of the UK and leaving the jurisdiction of the European Court of Justice.

Mr Raab, 44, was named Brexit secretary in July after the resignation of his predecessor David Davis, who also quit in protest at Ms May’s strategy.

At the heart of Mr Raab’s criticism was the belief that the pursuit of a temporary customs union with the EU would be the starting point for talks on the future relationship with the bloc, “severely prejudicing” what Britain could achieve.

European Union leaders were scheduled to meet on November 25 to endorse the divorce deal.

-with AAP