Ms Rayner announced earlier that day that she had settled her tax affairs with HMRC after a stamp duty row over her seaside apartment. But her team made clear she was not interested in the role, according to The Times. Ms Rayner did not speak to the Prime Minister directly at any point.

Downing Street went on to confirm that James Murray would take over as Health Secretary following Mr Streeting's exit.

It comes as the Prime Minister fights for his political future after a week of turmoil in the wake of the May elections.

Sir Keir is said to be privately considering whether he will defend his leadership if a contest were launched, despite having publicly vowed to stand against any challengers.

Greater Manchester Mayor Andy Burnham is seeking to run in the Makerfield by-election as he eyes a return to Westminster.

Speaking on Monday, Sir Keir insisted his focus was on delivering for the public who wanted the Government to “get on with the job” after the results earlier this month showed voters were “frustrated” with the pace of change.

The Prime Minister told staffers at Labour's headquarters: “We need to build up the urgency of what we do. We need a bit more hope in there. And we need to remember at all times what we are here to do.

“I am focused on the job that I was asked to do, which is to serve my country and to carry out my duties as Prime Minister of this country.

“Delivering for the very many people who voted us into office, who are saying: ‘Just get on with it, get on with the job, get on with the change that I need to see in my life.'”

Addressing the by-election, he added: “Whoever they are I am going to support them 100% and I want every member, everyone in our movement to support them. A Labour candidate to beat Reform. That is the fight that we are in.”