Welsh Secretary Simon Hart is part of a group of cabinet ministers thought to be about to tell Boris Johnson he should resign as Prime Minister.
The MP for Carmarthen West and South Pembrokeshire has entered Downing Street, as the slew of ministers' and parliamentary secretaries' resignations continues.
By Wednesday afternoon, 35 MPs had resigned from Boris Johnson's government.
The list comprises two cabinet ministers, 15 ministers, 15 parliamentary private secretaries, two trade envoys and one vice-chair.
With Mr Johnson's day going from bad to worse, he faced an intense grilling before the Liaison Committee on Wednesday afternoon, during which he ruled out calling an election - unless people "forget" his mandate.
Conservative MP for Preseli Pembrokeshire Stephen Crabb said he is "in no doubt whatsoever" that the majority of constituents support his own call for the Prime Minister to resign.
He said: "Over the last two months, every time I've been to the supermarket, every time I've done a surgery or a Q&A session, every day when I've opened up my email inbox I've had constituents - Conservative voters - telling me in no uncertain terms about their loss of faith and trust in the Prime Minister.
"It's very sad but we've got to a position now where the entire functioning of the government is gummed up and the Prime Minister does need to take a very brave decision to move on."
Mr Crabb admitted that he did not support Mr Johnson for leadership in 2019, but said he has displayed some "remarkable qualities".
"You've seen some of those qualities really come to the fore during the Ukraine crisis, which has allowed him to play to his strengths, he's shown a real clarity of purpose and real leadership.
"But all the while that that's happened, there's persistent allegations, questions, controversies that he's just been unable to draw a line under.
"I think for the good of the country - this isn't about the party anymore - for the good of the country he needs to resign quickly."
But Mr Johnson told MPs at PMQs that he is determined to remain Prime Minister.
Asked by a Tory MP whether there was any circumstance in which he would quit, the PM said: "The job of a prime minister in difficult circumstances when he has been handed a colossal mandate is to keep going and that's what I'm going to do."
A few hours later, Mr Johnson once again insisted at the Liaison Committee he will “of course” be prime minister on Thursday.