A junior Wales Office minister has quit over the prime minister's decision to turn to Jeremy Corbyn to try to get a Brexit deal through Parliament.
Nigel Adams said the decision was a "grave error" and the UK would now "end up in a customs union" with the EU.
Mr Adams, who was also a government whip, said he believed the UK would have coped with a "managed no-deal".
He became the fourth Wales minister to have the job within 12 months when he took up the role last November.
His resignation was followed by that of another minister, Chris Heaton-Harris, who quit saying his job at the Department for Exiting the European Union had become "irrelevant" if the government was not prepared to leave without a deal.
Later, Theresa May met Mr Corbyn to begin the process of seeing if they can formulate a deal both sides in Parliament can agree to.
The two leaders described the discussions as "constructive" and it is understood each party has appointed a negotiating team, which will meet later tonight ahead of a full day of discussions on Thursday.
In a speech from Downing Street the previous evening, Mrs May said if it was not possible to agree, they could choose a series of options to put to the House of Commons.
Wales' First Minister Mark Drakeford also held talks with the prime minister on Wednesday.
After the meeting he said the prime minister "seemed genuinely willing to listen, but of course at this late stage it's actions that matter if we are to avoid a no deal Brexit".
A Downing Street spokesperson said that in the meeting the prime minister "reaffirmed her commitment to working with MPs from across the political spectrum and they agreed that compromises needed to be reached in order to honour the result of the referendum".
Brexit Secretary Stephen Barclay has warned the "remorseless logic" of MP numbers in the Commons meant the UK was heading for an "undesirable" soft Brexit - closer links with the EU.
He blamed hard Brexiteers in the European Research Group of Conservative MPs who refused to back Mrs May's deal.
Mr Corbyn says he wants a customs union and workers' rights to be priorities and that he recognises his own "responsibility" to try to break the deadlock.
In his resignation letter, the MP for the Yorkshire seat of Selby and Ainsty warned Mrs May the government risked failing to deliver "the Brexit people voted for" and failing to prevent "the calamity of a Corbyn government".
"I and many others agreed with your previous position that no deal is better than a bad deal," he says.
"It now seems that you and your cabinet have decided that a deal - cooked up with a Marxist who has never once in his political life put British interest first - is better than no deal."
The resignation of someone no one in Wales has ever heard of..... another reason why the Wales Office should be abolished. https://t.co/DMEwMKSnBn— Alun Davies 🏴 (@AlunDaviesAM) April 3, 2019
Nigel Adams is the 30th UK Government minister to resign over Brexit in the past 12 months and the 35th in all.
In Prime Minister's Questions, Brexiteer Clwyd West MP David Jones questioned whether the PM still felt "that the leader of the opposition is not fit to govern".
She replied: "I do not think the Labour Party should be in government."
Welsh Secretary Alun Cairns said he was "disappointed to see Nigel leave government and would like to thank him for all his work and efforts as a minister".
"My department and I are committed to delivering on our priorities," he said.
Tory MP for Montgomeryshire Glyn Davies praised the MP. "I will miss working with him," he said.
But Labour Welsh assembly member Alun Davies said it was the resignation of "someone no one in Wales has ever heard of".
"Another reason why the Wales Office should be abolished," he tweeted.
Plaid Cymru Westminster Leader Liz Saville Roberts said the "almost constant churn of Wales Office ministers shows the fundamentally dysfunctional nature of this Westminster government".
"The people of Wales must be questioning whether the lack of consistency in the Wales Office is the reason why we are so invisible in the minds of the Westminster government," she added.
In a Facebook post Guto Bebb, Aberconwy MP, said he had "little respect left for colleagues such as Jacob Rees-Mogg, Dominic Raab or Boris Johnson" - who criticised Theresa May's deal only to later vote for it.
"Is it any wonder that politicians are held in contempt when they can go from high principle and emotive language to embracing something which is clearly in their view going to be bad for the UK just because they see an opportunity to become prime minister," he said.
He praised constituency neighbour David Jones, who Mr Bebb has clashed with in the past.
"It's well known that we do not agree on Brexit but at least we both stuck to our principles last week," he said.