His resignation as Brexit secretary deals a heavy blow to the stability of the prime minister’s administration, with two other ministers almost immediately following suit.

The departure of Mr Davis, Steve Baker and Suella Braverman, who had also served in the Department for Exiting the EU, could now embolden other senior figures to quit.

Ms May had been hoping to win over Brexiteers to her proposals agreed by the cabinet, including Mr Davis, on Friday – but since then Leave-backing Tory MPs have called for a change in leadership.

The move comes on the eve of a major test for the prime minister as she faces the house of commons on Monday, to explain her proposals, and then a stormy meeting of Conservative MPs.

In his resignation letter, Mr Davis wrote: “As you know there have been a significant number of occasions in the last year or so on which I have disagreed with the Number 10 policy line, ranging from accepting the [European] Commission’s sequencing of negotiations, through to the language on Northern Ireland in the December Joint Report.

“At each stage I have accepted collective responsibility because it is part of my task to find workable compromises, and because I considered it was still possible to deliver on the mandate of the referendum, and on our manifesto commitment to leave the Customs Union and the Single Market.

He went on to argue that the “general direction” of Ms May’s policies would leave the UK “in at best a weak negotiating position, and possibly an inescapable one”.

Mr Davis said the cabinet decision on Friday had ”crystallised this problem” and would hand control of “large swathes of our economy to the EU” and is “certainly not returning control of our laws” .