Britain's Secretary of State for Exiting the European Union David Davis leaves 10 Downing Street, London, January 29, 2018.
In a resignation letter circulated by local reporters, Davis told May he has repeatedly disagreed with the government over the previous year and that it is looking "less and less likely" that the government can deliver Brexit per voters' wishes.
The loss of her Brexit negotiator, and potentially another junior minister in the ministry, just two days after the meeting at May's Chequers country residence is a blow to the prime minister and underlines the deep divisions in her ruling Conservative Party over Britain's departure from the EU.
On Friday, Davis and the rest of May's fractious Cabinet finally agreed on a plan for future trade ties with the EU. Their stand may embolden pro-Brexit lawmakers to make a move against her.
"The general direction of policy will leave us in at best a weak negotiating position and possibly an inescapable one".
May's plan to adopt European Union regulations for all goods and agri-food products after Brexit "hands control of large swathes of our economy to the European Union and is certainly not returning control of our laws in any real sense", he said.
The responsibility for leading the negotiations should now go to an "enthusiastic believer in your approach, and not merely a reluctant conscript", he said.
In his resignation letter, he blamed the "dilution" of what he said was a firm Chequers agreement, delays to the White Paper, and omissions from the "backstop" customs proposal that would leave the United Kingdom in a "weak negotiating position at best".
She said she was "sorry" he was leaving but would "like to thank you warmly for everything you have done.to shape our departure from the EU".
In the Commons on Monday Mrs May is expected to tell MPs that the strategy agreed on by the cabinet at Chequers on Friday is the "right Brexit" for Britain.
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Their shipments will now be subject to a 25 percent tariff, which will instantly make their crops far costlier in China. The bloc argues that for some goods, such as trucks, U.S. import duties are higher.
It won the backing of one other high-profile Brexit campaigner.
The Brexit Secretary was understood to have serious reservations about both the plan and whether it could be acceptable to Brussels following the Chequers summit, but was absent from the television studios in the aftermath of the talks.
Mr Davis's resignation will anger cabinet colleagues from both wings of the party.
When the Conservatives returned to power in 2010, he never got a government post and spent his time on the backbenches campaigning on civil liberties issues.
Shortly afterwards he stood as the Conservative candidate and was re-elected.
Some Brexit-supporting lawmakers are angry at the proposals, saying they will keep Britain tethered to the bloc and unable to change its rules to strike new trade deals around the world.
The EU is not in a generous mood and views Mrs May's plan as "cherry-picking" from the single market to suit the British economy and the whims of Eurosceptic cabinet ministers. Her... "I assume he has resigned to speak".
Tweets from Sarah O'Grady, the wife of David Davis's chief of staff Stewart Jackson, suggested the veteran parliamentarian made the decision to walk away because he "couldn't sell out his own country".
"It is crucially important as it shows how well founded concerns over the Chequers conclusions are", he told Reuters.
Tory Andrew Bridgen said he could not support the proposals that came out of Chequers, describing them as a breach of the red lines and that he wouldn't support it "even if the European Union were paying us for it".