Speaking later to Sky News, Mr Dowden added that he did not think the Prime Minister should resign, regardless of the outcome of an civil service inquiry led by Sue Gray, a former head of propriety and ethics in the Cabinet Office.

The proposed reforms at the heart of Government come after six Tory MPs said they thought Mr Johnson should resign, while many more are thought to have submitted letters of no confidence to Sir Graham Brady, chairman of the 1922 committee.

For a leadership contest to be triggered, 54 letters of no confidence have to be submitted to Sir Graham – who does not reveal how many he has received.

It is thought about 20 may have been handed in, with the backbencher Tim Loughton indicating he could be persuaded to put his own thoughts into writing should the Prime Minister not quit in the “next few days”.

“It is not down to a simple Government policy change or a sacking of ministers or officials to put things right,” Mr Loughton wrote in a Facebook post on Saturday.

“In this case all roads lead back to Downing Street and the person whose name is on the front door.”

The Metropolitan Police have said it will delay and investigation into the alleged breaking of coronavirus laws until Ms Gray has completed her review.

Mr Dowden, who attends Cabinet as minister without portfolio, said the Government thought the “full extent” of lockdown-busting claims were in the public domain, but that Ms Gray had the power to delve into further allegations.

The Liberal Democrats have suggested that the House of Commons holds a no-confidence vote in the Prime Minister.

Wes Streeting, Labour’s shadow health secretary, said such a move would only “galvanise” the Conservatives because critical backbenchers would be forced to either break cover or publicly back Mr Johnson.

At least two Labour MPs have said that they would support such a vote nonetheless.