“If the Remain camp wins by a large majority, let’s say 60:40, then David Cameron might just survive. But if Remain win by a narrow majority or if Leave – as I certainly hope, I think – will win he’s toast within days."

Asked if Mr Cameron could do anything to win her back round, she added: “No and I will tell you why – because he’s lied profoundly and I think that is actually really at the heat of why Conservative MPs have been so angered.

“To say that Turkey is not going to join the Europe Union for as far as 30 years is a lie and if you look at what David Lidington, the minister, has said during the [Commons] debates in Hansard Turkey are well on the way to being part of the European Union.

“There are many issues about which David Cameron has told outright lies and the trust because of that has gone in both him and George Osborne. …

"So because of those very reasons the trust has been absolutely shattered in both David Cameron and George Osborne in the Conservative Party and it would be very hard for either of them to survive in the future.”

Asked about the possibility of a coup a Number 10 spokesman said: “The Prime Minister’s focus rightly is on the big issue facing the country – and that is do we remain part of the European Union or do we leave.

“He will be focused in the coming weeks purely on that – and taking the big decision that is right for the country. That is about jobs, prosperity and people’s livelihoods.

“It is quite clear that we are stronger, safer and better off in. That is what the Prime Minister will be focused on – we will leave it to others to explain what they’ll be focused on.”