British Prime Minister Boris Johnson has told MPs he would "keep going” despite a growing list of Conservative ministers and other officials resigning in protest over his handling of the case of a senior official accused of sexual misconduct.

A delegation of Cabinet ministers planned to meet with Johnson at his Downing Street office on Wednesday evening to press him to resign, according to British media reports. Transport Secretary Grant Shapps and longtime loyalist Brandon Lewis were among those expected to demand that he quit.

"The job of a prime minister in difficult circumstances when you’ve been handed a colossal mandate is to keep going. And that’s what I’m going to do,” Johnson said earlier at the weekly session of Prime Minister’s Questions in parliament.

David Davis, a Conservative legislator who had previously called on the 58-year-old leader to resign, told parliament that he was again asking Johnson: "to do the honourable thing, to put the interests of the nation before his own interest, and before … it does become impossible for government to do its job.”

Johnson said he did not believe that it was against the national interest for him to remain as prime minister.

"I thank him very much for the point he’s made again. I just couldn’t disagree with him more,” Johnson said.

Later on Wednesday, James Duddridge, a Conservative lawmaker and close aide of Johnson, told Sky News the British leader "is buoyant, he is up for a fight” after a meeting with members of his top cabinet team.

Duddridge said Johnson and the newly-appointed finance minister Nadhim Zahawi would set out a new joint plan for the economy next week which would include tax cuts.

Johnson sacked Michael Gove, a senior minister who media earlier said had told the British leader he should quit.

On Wednesday night, Secretary of State for Wales Simon Hart joined those resigning.

The attorney general for England and Wales, Suella Braverman, also called on Johnson to resign and became the first cabinet minister to say they would run to replace him in any Conservative Party leadership contest.

"I do think the time has come for the prime minister to step down,” Braverman said on ITV. She said she did not want to resign from her post. "If there is a leadership contest I will put my name into the ring.”