Sir Bob Neill, also a select committee chair, said he has submitted a letter of no confidence in Johnson, arguing a “change in leadership is required” to restore trust in politics.
He said: “Trust is the most important commodity in politics, but these events have undermined trust in not just the office of the prime minister, but in the political process itself.”
Prior to Neill’s announcement, four MPs called for Johnson to go since Sue Gray’s damning report was published on Wednesday.
Several other Tory MPs had previously demanded the PM step down.
It takes 54 MPs to submit letters Sir Graham Brady, chair of the 1922 committee of backbench Conservatives, to trigger a no confidence vote in Johnson, which would force a leadership contest.
Alicia Kearns, a Conservative elected to the Commons in 2019 during Johnson’s landslide election victory, also reaffirmed that her leader had lost her confidence.
Also on Friday, Tory MP Paul Holmes quit his government job over the “deep mistrust” voters now have in the Conservative Party.
Neill, who chairs the Commons justice committee, said he had waited to read the senior civil servant’s full report into No 10 lockdown parties before making up his mind but said he found the prime minister’s explanations for his behaviour lacked credibility.
Posting a statement on his website, the MP for Bromley and Chislehurst said: “I have listened carefully to the explanations the prime minister has given, in parliament and elsewhere, and, regrettably, do not find his assertions to be credible.
“That is why, with a heavy heart, I submitted a letter of no confidence to Sir Graham Brady on Wednesday afternoon.
“Trust is the most important commodity in politics, but these events have undermined trust in not just the office of the prime minister, but in the political process itself.
“To rebuild that trust and move on, a change in leadership is required.”
Meanwhile, Kearns said the prime minister’s “account of events to parliament” about No 10 lockdown parties was “misleading”.
The Rutland and Melton MP said in a Facebook post: “It is wrong that families were banned from saying goodbye to their dying loved ones, whilst the prime minister was complicit in the holding of many goodbye parties for his staff, which we now know displayed a complete disregard for restrictions and were complete with vomiting, fighting and bullying.
“I can only conclude that the prime minister’s account of events to parliament was misleading.
“If he did not know about the culture of parties, then this is because he failed to ask the questions necessary, or has chosen not to since last October.
“Those around him clearly did not advise a policy of being honest and transparent with the British people.”
Kearns added: “My position remains unchanged since January, and the prime minister continues not to hold my confidence.”
Sue Gray’s partygate report painted a debauched picture of booze-fuelled lockdown partying into the early hours, cleaners having to scrub red wine off the walls, a fight between staff, and a karaoke machine at the ready.