Responding to the row, Streeting likened the claims to conspiracy theories and demanded that Starmer sack whoever was responsible.
This week, calls for sackings continued to grow.
Ed Miliband, the Energy Secretary and former Labour leader told BBC Radio 4’s Today programme: “I think you get briefings that happen in politics, they’re an unfortunate part of politics, I deplore the culture of briefing.”
Asked whether the Prime Minister should sack anybody found to have been involved in the briefings, Miliband replied: “Of course he should.”
But Alastair Campbell, Sir Tony Blair’s former director of communications, told the Downing St operation: “There are bigger, worse enemies, like Nigel Farage ... Get a grip.”
Morgan McSweeney, a pivotal figure behind Labour’s 2024 election victory, is now facing calls to resign.
One Cabinet minister told the Times: “If the PM didn’t approve it, he needs to get rid of Morgan.”
But other ministers are rallying round McSweeney. Another Cabinet minister told the Telegraph: “Morgan is brilliant, and decent.
“He’s an obvious person to point to, as everyone will want an easy response to a s*** day.
“But this is more a problem of political culture. Endless speculation, comment and pages to fill and a few too many people happy to fill them with nonsense.”
The Cabinet minister added: “He doesn’t deserve to be sacked, especially not for this. He’s good.”
Asked if the briefings should result in sackings, Rachel Reeves, the Chancellor, said: “Well, there I think is going to be a leak inquiry, but at the moment there is no evidence of where that briefing is coming from.”
Lord Glasman, a Labour peer and close ally of Starmer’s chief of staff, claimed plotters had been trying to oust him from No 10.
He told GB News: “I don’t think civil war is overblown, but everybody knows there’s blue Labour and there’s new Labour and there’s a contestation.”
Streeting refused to discuss the briefing war, saying that the public did not “give two monkeys” about “Westminster bubble stuff”.
During a visit to Liverpool, he said: “I have no intention of revisiting yesterday’s events. That’s yesterday’s news and it’s Westminster bubble stuff that doesn’t mean anything to anyone.”
The Prime Minister and Streeting talked by phone on Wednesday evening. Starmer, who the Telegraph understands is infuriated by the briefings, is said to have apologised for the events in a brief conversation.
Anna Turley, the Labour Party chairman, said people were “investigating” who was behind the leaks.
Starmer has faced questions over his leadership for some months. The row over Streeting’s supposed ambitions follows speculation at Labour’s party conference in September that Andy Burnham, the Mayor of Greater Manchester, was preparing to challenge the Prime Minister.
This latest saga has reinforced the jittery mood in No 10, and the disillusionment felt by many Labour MPs about their party’s unpopularity, before a Budget which is expected to break a key election manifesto by raising income tax.
During the shake-up of Downing St in September, it was reported that Starmer considered making McSweeney report to Darren Jones, the new chief secretary to the Prime Minister. The move, which would have widely been seen as a demotion, did not take place.
Supporters of McSweeney have long floated the idea that at some point in this Parliament, he could take a role more focused on winning Labour re-election rather than helping manage the Prime Minister’s time in office.
For months, some Labour figures have also played down the idea that Starmer could completely part with his chief of staff, given McSweeney’s political nous and what is seen as the Prime Minister’s lack of natural political strategic instincts.
In recent political history, top aides to prime ministers who find themselves dominating the headlines have tended to leave No 10 before too long.
Dominic Cummings, who spectacularly fell out with Boris Johnson in office, and Alastair Campbell, Sir Tony Blair’s director of communications, both left Downing St after months of media coverage regarding the power they held behind the scenes.
Sign up to Herald Premium Editor’s Picks, delivered straight to your inbox every Friday. Editor-in-Chief Murray Kirkness picks the week’s best features, interviews and investigations. Sign up for Herald Premium here.