His resignation as Brexit secretary deals a heavy blow to the stability of the prime minister’s administration, with another minister immediately following suit.
The departure of Mr Davis and Steve Baker, 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.
“I am afraid that I think the current trend of policy and tactics is making that look less and less likely.”
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” .
Ms May responded saying she disagreed with his “characterisation” of the agreement reached at Chequers last week.
She said: ”I am sorry that you have chosen to leave government when we have already made so much progress towards delivering a smooth and successful Brexit, and when we are only eight months from the date set in law when the United Kingdom will leave the European Union.”
Mr Davis had also written to the prime minister ahead of the crunch cabinet meeting last Friday, warning that her proposals would not be accepted in Europe.
He is also said to have been annoyed after being sidelined in negotiations by Ms May’s civil servant Europe advisor Olly Robbins.
But Daily Express correspondent Sarah O’Grady, the wife of Mr Davis’ special adviser Stewart Jackson, said “DD decided he couldn’t sell out his own country”.
Jacob Rees-Mogg, who chairs the Brexit-backing European Research Group of Tory backbenchers, said: “This is very important.
“It raises the most serious questions about the PM’s ideas. If the Brexit secretary cannot support them they cannot be very good proposals.
Turning his fire on the meeting at Chequers on Friday, he said: “It was an attempt to bounce the cabinet. It was a serious mistake.”
Backbencher Peter Bone also supported Mr Davis’ decision to quit, saying he had “done the right thing” and that it was a “principled and brave decision”.
He added: “The PM’s proposals for a Brexit in name only are not acceptable.”
Mr Baker, a key Tory figure in the Leave campaign, was Mr Davis’s main lieutenant at Dexeu, and was hailed as ”courageous and principled” by other Brexiteer Tories as he also left.
Ms May is expected to tell MPs at what may now become a critical meeting on Monday, that the strategy agreed on at Chequers is the “right Brexit” for Britain.
Her plans would commit the UK to maintain a “common rule book” with the EU, meaning it would effectively seek to stay in a single market for goods, for the foreseeable future at least.
The proposed facilitated customs arrangement, would see all imported goods charged the UK tariff at the border, with goods then tracked and if they were sent on to the continent, exporters would be charged the EU tariff with money passed on to Brussels.
The plan means that the UK can theoretically sign trade deals with other countries in which it promises to lower tariffs on goods, in return for preferable access for its services. But the promise not to deviate from EU standards on goods, means a change to regulations could not form a part of any trade deal – something which has angered Brexiteers.
Some Conservatives told The Independent they believed there could be enough disgruntled MPs willing to trigger a leadership contest in a bid to remove Ms May.
But even if the 48 needed to oust Ms May materialised, a poll for The Independent showed a majority of the public would expect a general election to be called if Ms May goes.
Labour’s shadow education secretary Angela Rayner said: “David Davis resignation now shows the Tory party is in complete disarray and not governing in the national interest.
“This nonsense cannot continue, even the Tory spin doctors cannot surely spin a positive message out of this debacle.”
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