Sajid Javid as resigned as health secretary and Rishi Sunak as chancellor, as Boris Johnson faces growing pressure over his handling of the Chris Pincher affair.
In his letter, Javid wrote: "The tone you set as a leader, and the values you represent, reflect on your colleagues, your party and ultimately the country. Conservatives at their best are seen as hard-headed decision makers, guided by strong values. We may not always have been popular, but we have been competent in acting in the national interest. Sadly, in the current circumstances, the public are concluding that we are neither."
Sunak wrote: "To leave ministerial office is a serious matter at any time. For me to step down as chancellor while the world is suffering the economic consequences of the pandemic, the war in Ukraine and other serious challenges is a decision that I have not take lightly.
He added: "However, the public rightly expect government to be conducted properly, competently and seriously. I recognise this may be my last ministerial job, but I believe these standards are worth fighting for and that is why I am resigning.
"I have been loyal to you, I backed you to become leader of our party and encouraged others to do so. I have served as your chancellor with gratitude that you entrusted me with stewardship of the nation's economy and finances. Above all, I have respected the powerful mandate given to you by the British people in 2019 and how under your leadership we broke the Brexit deadlock."
The letter went on: "That is why I have always tried to compromise in order to deliver the things you want to achieve. On those occasions where I disagreed with you privately, I have supported you publicly. That is the nature of the collective government upon which our system relies and it is particularly important that the prime minister and chancellor remain united in hard times such as those we are experiencing today."
The resignations come after a former Foreign Office permanent secretary said Boris Johnson was briefed in person on alleged wrongdoing by Tory MP Chris Pincher.
In a letter to the parliamentary standards commissioner, Simon McDonald said No.10 was "not telling the truth" about the situation.
It came after a slew of new allegations of misconduct against Pincher over the weekend since his resignation from government and subsequent removal of the Conservative Party whip after his drunken actions at the private Carlton Club in London on Wednesday.
In an interview that went public at the same time as the resignations, Johnson defended Pincher's actions, saying: "Let me explain what happened. We are talking about a series of appointments over seven years.
"Chris Pincher came into government as deputy chief whip before I became prime minister, he was moved to the Foreign Office, he then went on to be a minister for housing and we then moved him back to be deputy chief whip.
"About two and a half years ago I got this complaint, it was something that was only raised with me very cursorily but I wish that we had, I in particular, had acted on it and that he had not continued in government because he then went on, I'm afraid, to behave, as far as we can see, according to the allegations that we have, very, very badly.
"I'm sorry for those who have been badly affected by it."
Adam Payne is political editor of CSW's sister title PoliticsHome, where this story first appeared