Brexit Secretary David Davis, who has been leading negotiations to leave the EU, has resigned from the government.
In his resignation letter, Mr Davis criticised the PM’s Brexit plan – agreed by the cabinet on Friday – saying it would leave Parliament with “at best a weak negotiating position”.
In her reply, Mrs May said she did not agree but thanked him for his work.
Junior minister Steve Baker quit shortly after Mr Davis – as Mrs May prepares to face MPs and peers later.
The UK is due to leave the European Union on 29 March 2019 but the two sides have yet to agree how trade will work between the UK and the EU afterwards.
In his letter, Mr Davis told Mrs May that “the current trend of policy and tactics” was making it “look less and less likely” that the UK would leave the customs union and single market.
He said he was “unpersuaded” that the government’s negotiating approach “will not just lead to further demands for concessions” from Brussels.
Mr Davis, who was appointed Brexit Secretary in 2016, said: “The general direction of policy will leave us in at best a weak negotiating position, and possibly an inescapable one.”
In her reply, Mrs May said: “I do not agree with your characterisation of the policy we agreed at cabinet on Friday.”
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”.
Eurosceptic MP Mr Baker played a leading role in the Brexit campaign in the run up to the 2016 referendum. He was promoted to the Department for Exiting the EU as a parliamentary under-secretary in June last year.
Conservative MP Peter Bone hailed Mr Davis’s resignation as a “principled and brave decision”, adding: “The PM’s proposals for a Brexit in name only are not acceptable.”
Labour Party chairman Ian Lavery said: “This is absolute chaos and Theresa May has no authority left.”
Labour leader Jeremy Corbyn said Mrs May was “incapable of delivering Brexit”.