In his resignation letter, he argued that the prime minister's latest plan was a signal to the Brexit-voting public that the referendum was being betrayed by too soft an exit strategy from the EU.
But at an earlier session of parliament, May stood firm after being challenged by one pro-Brexit lawmaker in her party to explain when she had made a decision to change her catchphrase from "Brexit means Brexit", to "Brexit means Remain".
The talks follow an extraordinary fortnight for the Government in which the Cabinet agreed a compromise deal on Brexit only for Mr Davis and Boris Johnson to quit Mrs May's top team as a result.
He told MPs: "Given that in important ways this is Brexit in name only, I am of course unable to support it and am happy to be able now to speak out against it".
May is battling to unite her Conservative Party around her Brexit blueprint formally unveiled last week following months of cabinet infighting.
But a mini-rebellion within the Conservative party has led to the amendment to the Trade Bill, which will require the government to push for membership of the EMA in the forthcoming Brexit negotiations.
It has been confirmed that Mr Johnson will make his resignation speech to the House of Commons following PMQs, a source close to the former foreign secretary has said.
"We have time in these negotiations".
The amendment would have required the government to try to negotiate a customs union arrangement with the EU if, by January 21, 2019, it had failed to negotiate a frictionless free trade deal with the bloc.
The PM also rejected a call from SNP leader Ian Blackford to extend the Article 50 period, a move which would give the United Kingdom more time to negotiate a deal with the European Union before Brexit becomes official.
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Trump claimed on June 13 that North Korea was no longer a nuclear threat, just a day after his meeting with Mr. It is unknown whether the North Korean side gave any prior notification to the U.S. about this.
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After her 90-minute grilling at the liaison committee May faced a meeting of her backbenchers, winning support from majority.
Writing in the Daily Telegraph Mr Timothy said that if Britain leaves the European Union in "chaos" or does not leave the bloc at all, "a national humiliation greater than Suez awaits".
"At absolutely no point because BREXIT continues to mean BREXIT", Mrs.
"A fog of self-doubt has descended", he said.
It on top of another very hard day for the prime minister, after narrowly surviving a key vote on the customs union last night, and caving to the demands of hardline Tory Brexiteers in a series of votes on Monday.
"If we get distracted by individual amendments to individual pieces of legislation. then I think we get dragged into an unnecessary debate that wastes a lot of time and energy", Foreign Minister Simon Coveney told Ireland's state broadcaster RTE.
"We have got a mission in government and it is serious".
Although the government succeeded in rejecting the amendment, Tory Brexiteer Andrew Bridgen said that if the PM had lost the vote it "would have triggered a confidence motion in the government immediately", according to Sky News.
Boris Johnson put down a clear marker of his leadership ambitions on Wednesday after he tore into Theresa May's Brexit proposals, branding them "miserable" and a "democratic disaster".
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