Two more ministers resigned from the UK government on Wednesday, piling further pressure on Prime Minister Boris Johnson following the departure of his health and finance ministers.

Will Quince, minister for children and families, said he had "no choice but to tender my resignation" while junior transport minister Laura Trott said she was quitting over a loss of "trust" in the government.

"With great sadness and regret, I have this morning tendered my resignation to the Prime Minister after I accepted and repeated assurances on Monday to the media which have now been found to be inaccurate. I wish my successor well – it is the best job in government," Will Quince tweeted.

This comes hours after Boris Johnson named his health secretary Nadhim Zahawi as the new finance minister and Steve Barclay as the new health secretary after the shock resignations of Rishi Sunak and Sajid Javid.

Both finance minister Rishi Sunak and health minister Sajid Javid resigned in what appeared to be a choreographed release of letters to the prime minister, in which both took aim at his ability to run an administration that adhered to standards.

The resignations came as Johnson was apologising for what he said was a mistake for not realising that a former minister in charge of pastoral care was unsuitable for a job in government after complaints of sexual misconduct were made against him.