Mr Kwarteng was asked whether he would have used the same words as the Prime Minister.

He told Trevor Phillips On Sunday on Sky News: “I think it’s entirely legitimate… it depends what the context was.

“In that context, I think it was perfectly reasonable to mention the fact that Sir Keir had apologised.

“Sir Keir himself apologised on behalf of the organisation that he led about the fact that they failed to prosecute Jimmy Savile.

“So the fact that he apologised suggests that he does at some level bear some responsibility.”

Mr Kwarteng said he was not saying Sir Keir had “personal blame”.

‘It was a stupid thing for the PM to do’

Lord Barwell told the same programme: “Even if you set aside that moral argument, on a purely tactical level it was a stupid thing for the Prime Minister to do.

“Because it’s led to the resignation of one of his key aides, it’s led to more MPs submitting letters of no confidence in him. It’s further destabilised his position.

“The point here is that we know he was given advice not to do that, and went ahead and did it anyway.

“What that tells you is that yes, having the right people around you can help. But ultimately, the culture at No 10 and the decisions the Government makes come from the top.

“The Prime Minister himself, if he’s going to stay in office, is going to have to change the way he is behaving and running the Government.”

Rishi Sunak, the Chancellor, and Sajid Javid, the Health Secretary, have both indicated they would not have said the remarks, although Mr Kwarteng told T&G on Times Radio: “I don’t think they were criticising the Prime Minister.

“They were making a specific point about what they would have done in the course of a debate, and I don’t think that’s a criticism of anybody.”

One of Mr Johnson’s most loyal aides, Munira Mirza, quit as No 10’s head of policy over his use of the “scurrilous” Savile smear against Sir Keir.

Lawyers representing Savile’s victims have also criticised the Prime Minister.