Wes Streeting has said suggestions from the prime minister’s allies that he is seeking to challenge for the leadership are “self-defeating nonsense” and has urged Sir Keir Starmer to sack whoever is briefing the media.

On Tuesday evening, friends of Sir Keir had told several news outlets his job might be under immediate threat and that they were particularly suspicious of Streeting’s leadership ambitions.

Speaking to the BBC on Wednesday, the health secretary said he could “not see any circumstances under which I would do that to our prime minister”.

He added that briefings to the press against him were “the worst attack on a faithful since Joe Marler was banished in The Traitors final”.

“Someone has definitely been watching too much Celebrity Traitors. They should swap to Countryfile,” he said.

Streeting was doing a round of media interviews on a morning with newspaper headlines dominated by the briefings from the prime minister’s allies, suggesting a leadership rival could make their move after the Budget in two week’s time.

The health secretary insisted he was “not challenging the prime minister” adding: “I’m not doing any of the things some silly briefer said overnight.”

He said the culture in No 10 was “toxic” and that Lucy Powell, the party’s new deputy leader, had been right to call for a change of culture in Downing Street.

“I’d like to commend the briefer on at least picking on one of the men in the cabinet instead of the women,” he added.

Asked if he should sack those responsible, Streeting said: “Yes. But he’s got to find them first and I wouldn’t expect him to waste loads of time on this.

“There are people around the prime minister who do not follow his model and style of leadership.”

Other names being discussed as potential candidates in a leadership race include Home Secretary Shabana Mahmood, Energy Secretary Ed Miliband and backbenchers including former Transport Secretary Louise Haigh.

Sources close to Mahmood have said the idea she is planning to challenge Sir Keir for the leadership is “nonsense”.

“He will fight this,” one minister said, before making reference to a key by-election in 2021 which Labour lost to the Conservatives, prompting Sir Keir to consider resigning as Labour’s leader.

“This is not a Hartlepool moment,” they added.

“He is one of only two people alive who have won a general election for Labour. It’d be madness to run against him after 17 months.”

Challengers for the Labour leadership can initiate an election with the support of 20% of the party’s MPs, which currently means 80 nominations would be needed.

In order to trigger a leadership contest against the prime minister, challengers would need the support of 20% of Labour MPs, which currently means 81 nominations would be required.

Supporters of the prime minister have argued a leadership contest would plunge the party into the chaos associated with the last years of the previous Conservative government.

They are trying to convince their colleagues that a contest could destabilise the international markets too, and would jeopardise the relationship the prime minister has established with President Trump.

Jo White MP, chair of Red Wall Labour backbench group, told the Today programme this was “neither the time or the place” for briefings about a leadership challenge.

“This is a group of people who think they’re much cleverer than the rest of us, who spend their time selectively briefing journalists and stirring the pot.

“I want to simply say: we’re not having it.

“I’d like to say to No 10, I think they’re barking up the wrong tree, briefing against Wes.”

The BBC has been told that the strategy of Downing Street’s director of communications had been for different cabinet ministers to make one big intervention each week ahead of the Budget on 26 November.

One Labour insider said it was “bonkers” and “unhinged” that, due to the briefings from the PM’s allies, Streeting ended up facing questions about Sir Keir’s political future rather than his plans for the NHS.

Allies of Streeting have questioned whether the briefing was sanctioned by the PM and described No 10 as an “unhappy house”.

Despite winning a landslide majority in the July 2024 general election, Sir Keir has had a rocky time in Downing Street and opinion polls suggest he is unpopular.

There have been suggestions the government could face a crunch point after devolved elections in Scotland and Wales and local elections in England next year.

One senior Labour MP told the BBC: “It’s all very well to say wait for the locals, but that’s my activist base I’m sending into the gunfire. I can’t lose all my councillors.”

Another Labour source said: “The list of reasons for people to move after the Budget are growing by the day.

“If Wes is brave and moves he may well be rewarded by being prime minister by Christmas.”

Additional reporting by BBC political correspondent Iain Watson.