Brexit minister Chris Heaton-Harris quit his post on Wednesday, telling the PM: “I simply cannot support any further extension to Article 50 and this obviously means I cannot stay in government.”
He added: “I truly believe we should have honoured the result of the 2016 referendum” and left the EU on March 29.
It came as Mrs May and Mr Corbyn met in her Commons office on Wednesday afternoon in the hope of agreeing a position which can win a majority within the next few days, allowing her to request a short delay to Brexit at next week’s EU summit.
The Labour leader reportedly said the meeting had gone “very well” and that he expected more talks soon.
In a tweet, alongside his resignation letter, Mr Heaton-Harris said: “After much contemplation, I have decided to leave Theresa May’s Government.
“I’m grateful to the PM for giving me the opportunity to serve the UK and I will continue to represent my constituents as the MP for Daventry.”
He added in his letter that, as a Brexit minister, “I’ve had the responsibility of helping to coordinate our preparations for if we were to leave the European Union without a negotiated deal”.
“These preparations are well advanced and whilst I would have preferred to leave the European Union with your deal, I truly believe our country would have swiftly overcome any immediate issues of leaving without a deal and gone on to thrive,” he told Mrs May.
He continued: “However, I completely understand you do not want to leave the European Union without a negotiated deal and that obviously makes my job in Government irrelevant.”
The Minister for Wales, Nigel Adams, also resigned over Mrs May’s plans for a compromise deal with the Labour leader in order to make progress on Brexit.
He said the PM had made a “grave error” by reaching out to Mr Corbyn in the hope of finding a consensus on Brexit ahead of a crunch EU summit on April 10.
As the pair met for talks, leaders and spokesmen of other opposition groups agreed to make a People’s Vote their priority.
In a joint statement, the SNP’s Westminster leader Ian Blackford, Liberal Democrat leader Sir Vince Cable, Green MP Caroline Lucas, Plaid Cymru Westminster leader Liz Saville-Roberts and The Independent Group spokesman Chuka Umunna said: “We are in agreement that there is no such thing as a good Brexit and that people across the UK face being worse off.
“We have shown over the past three years we are willing to find a compromise position to end the impasse.
“Time is fast running out and any compromise that is reached must be brought back to the people through a fresh referendum, and keep the option to revoke Article 50 on the table to avoid a no-deal Brexit.”
Mrs May’s offer to try and end the impasse over EU withdrawal has sparked fury among Tory Eurosceptics.
She said last night that she will seek an Article 50 extension beyond next week to allow negotiations with Mr Corbyn aimed at ensuring the UK leaves the EU “in a timely and orderly way”.
Mr Corbyn said he would be “very happy” to meet the PM in a bid to offer “certainty and security” to the British people.
Leading Brexiteer Jacob Rees-Mogg described her offer as “deeply unsatisfactory” and accused the Prime Minister of planning to collaborate with “a known Marxist”.
And normally-loyal Caroline Johnson joined a clutch of Tory backbenchers at Prime Minister’s Questions today who spoke out against what she called “the risk of letting down the country and ushering in a Marxist, anti-Semite led government”.