David Davis’ resignation on Sunday came only two days after May had secured approval from her cabinet to negotiate “a business-friendly” deal to leave the EU.
In his resignation letter, the Secretary of State for Exiting the EU said he did not want to be a “reluctant conscript” and that he thought the plan approved on Friday “is certainly not returning control of our laws in any real sense”.
May has struggled to unite factions within her ruling conservative party.
In a letter responding to Davis’ resignation, she said she was “sorry” he had chosen to resign and argued her proposal was “consistent with the mandate of the referendum”.
Junior Brexit Ministers Steve Baker and Suella Braverman resigned shortly after Davis.
The hard-won proposal was agreed to at May’s Chequers country retreat after marathon talks on Friday.
In a statement released late on Friday evening, May said the 26 cabinet members in attendance reached a “collective” agreement that would see the UK agree to negotiate a “common rulebook for all goods” in a combined customs territory.
May said her cabinet also agreed to negotiate regulations for industrial and agri-food goods, ending the free movement of people, the supremacy of the European court and “vast” payments to the bloc.
Tory Brexiteers have voiced concern about the agreement, with the chairman of the campaign group Leave Means Leave accusing May of personally deceiving Brexit campaigners.
“May’s Brexit means BRINO – ‘Brexit In Name Only’ – a fake Brexit,” John Longworth said.
Jacob Rees-Mogg, a key figure in the conservative party’s “hard Brexit” faction which supports relinquishing access to the EU’s single market in exchange for full border control, said the deal would be “worse” than a UK exit from the EU with no deal at all.
“A very soft Brexit means that we haven’t left, we are simply a rule-taker,” he told BBC Radio 4’s Today programme on Saturday.
Responding to Davis’ resignation, pro-Brexit MP Andrea Jenkyns in a tweet praised him for “having the principal and guts to resign”.
Jeremy Corbyn, the leader of the opposition Labour party, said the resignation was proof May “has no authority left and is incapable of delivering Brexit”.
“With her Government in chaos, if she clings on, it’s clear she’s more interested in hanging on for her own sake than serving the people of our country,” he tweeted.
David Davis resigning at such a crucial time shows @Theresa_May has no authority left and is incapable of delivering Brexit.
With her Government in chaos, if she clings on, it's clear she's more interested in hanging on for her own sake than serving the people of our country.
— Jeremy Corbyn (@jeremycorbyn) July 8, 2018
Thomas Brooks, a professor of law and government at Durham University, told Al Jazeera the resignation was “very bad” for Britain’s embattled prime minister and “calamitous” for the country’s Brexit negotiations.
Citing previous calls for a leadership challenge, Brooks said he would not be surprised if Davis himself challenged May or put his support behind someone else.
“There’s going to be a challenge almost certainly in the next hours or days,” Brooks said.