The controversial debate on Brexit eventually led to the resignation of former Prime Minister David Cameron. But he denied mounting a coup and said he was not putting himself forward as her successor.
Two more junior ministers - Suella Braverman at the Brexit Department and Shailesh Vara at Northern Ireland - also quit along with two parliamentary aides.
His move is expected to be matched by other members of the ERG, hugely increasing the chances of Mrs May facing a vote of no confidence in her leadership.
Steve Baker, a ringleader of Tory Brexiteers, said he had been speaking to colleagues and his count was "a little over 48" with another dozen "probable" - although he acknowledged this may be inaccurate as only Sir Graham knew the true figure.
If such a motion passed, a new government would have to be formed within 14 days and win a confidence vote in the Commons.
She defended her deal as "what's right for the people of this country" and "the national interest". Her Conservatives don't have a parliamentary majority, and whether she can persuade enough lawmakers to back the agreement is uncertain.
Confronted in her constituency by Sky News, Mrs Leadsom said she was "absolutely determined to support the PM in getting the best possible deal for the United Kingdom as we leave the EU".
Leave-supporting Mr Barclay's job will be limited to the domestic delivery of European Union withdrawal, preparations for Brexit either with or without a deal and shepherding legislation through Parliament.
But chief whip Julian Smith later told reporters Mrs May would not be budged. "The Prime Minister will not be bullied and will not change course".
She also laid into political opponents, saying their ideas for resolving the biggest stumbling block in EU-U.K. negotiations - avoiding a hard border between Northern Ireland and the Republic of Ireland after Brexit - wouldn't resolve the problem. So far, more than 20 lawmakers have publicly said they submitted such letters.
Dismissing Mrs May's plan, he said: "This is not Brexit. Government policy is Government policy", she told LBC. While she received backing from senior ministers, the proposal was rejected by the opposition and members of her party. It is too late.
The new Work and Pensions Secretary immediately began efforts to shore up Mrs May's embattled position, telling Conservative MPs: "This is not a time for changing our leader".
"It would be politically unsustainable for any government to deliver a no deal without the consent of Parliament".
Sterling dropped 1.5% to just below 1.28 United States dollars and was 1.4% lower at 1.13 euro.
The Prime Minister's critics believe they have the numbers required to trigger a confidence vote within days.
He also said he could not accept "an indefinite backstop arrangement" for the Irish border.
Leadsom told Sky News Saturday "there is still more to be done" to get "the best possible deal for the U.K." before the draft withdrawal agreement is signed off on November 25 in Brussels.
More than two years after the United Kingdom voted to leave the European Union, it is still unclear how, on what terms or even if it will leave as planned on March 29, 2019. "I could not look my constituents in the eye were I to do that". "We are waiting for the same situation in London, but here in Brussels it will survive".
He sent a message to the British people: "As much as I am sad to see you leave, I will do everything to make this farewell the least painful possible, both for you and for us".