Sir Keir Starmer has a month to prove that his Government is not “fundamentally” dysfunctional, a senior Whitehall figure has said.

In a warning shot to the Prime Minister, the source said Sue Gray was “not of the party” and that only he could get a grip on the worsening situation.

The remarks come amid a bitter briefing war between top figures in Downing Street, and a public row over donations to Cabinet ministers.

On Saturday night, a No 10 source dismissed suggestions of a split and insisted the Government was “laser-focused” on delivering on voters’ priorities.

A poll on Saturday showed that Sir Keir’s approval rating had plummeted to its lowest level, and he was now more unpopular than Rishi Sunak.

One well-connected source said figures close to the Prime Minister had been warned he needed to personally intervene and “get a grip” on the crisis.

“If this is continuing in four weeks time then there’s something fundamentally wrong,” the Whitehall figure told The Telegraph. “That will show how dysfunctional it is, or whether it’s just growing pains that they do need to sort out. They have not handled it well, to be honest.”

The source said the unrest must not be allowed to overshadow Rachel Reeves’ first Budget, which will take place on Oct 30.

Sir Keir is facing growing discontent within Labour. Ms Gray, his chief of staff, has been the target of attacks including the leaking of her salary, which revealed that she is paid more than the Prime Minister.

Reports have also repeatedly surfaced suggesting that No 10 has split into three rival camps, all of which are vying for power over Sir Keir.

Morgan McSweeney, his top political adviser, and Simon Case, the Cabinet Secretary, are both said to have clashed with Ms Gray. Her role has been the subject of repeated anonymous briefings that she is wielding huge power over the Prime Minister.

The leaks have come against the backdrop of huge anger among advisers who have seen their pay cut compared to when Labour was in opposition.

Ms Gray has been blamed by many after it emerged that she has been placed in a new top salary band, meaning she is able to earn £170,000. In contrast, many special advisers entering government departments have been put on a flat wage packet of £57,000, meaning their earnings went down.

One source said many more junior advisers were “royally  f—ed off” by the situation, while another admitted that it had “caused a lot of resentment”.

On Saturday night it was also claimed that of the 12 officials in Sir Keir’s office, three have already quit and five have asked to be moved, with fingers pointed at Ms Gray. She has been defended by allies, who insist she is not responsible for the row over pay and has been blamed for decisions she did not make.

Cabinet ministers also rallied around her amid rumours that she could even quit because she has become so fed up with the public attacks on her.

Peter Kyle, the Science Secretary, who is a close ally of Sir Keir, told The Telegraph in an interview that Ms Gray was an “outstanding public servant”.

“I’m not sure why it’s a surprise to anyone that the chief of staff to the Prime Minister is powerful,” he said in response to the criticism of her. “I think it would be far more worrying for our country if the chief of staff to the Prime Minister was weak.”

‘A human shield’ for the Prime Minister

A Labour MP also defended Ms Gray, saying she had become a “human shield” for the Prime Minister and describing her as a “very tough cookie”.

“I have no doubt that Starmer-sceptic forces are trying to remove Sue Gray on the one hand and that she is a kind of human shield for him on the other,” said the MP. “The bottom line is they have no confidence in Keir and think if they weaken her then they can control or even remove him at a time of their own choosing.”

But she was criticised by Lord Blunkett, a former home secretary, after it emerged that she had been advised to lower her salary below Sir Keir’s but refused to.

He told Times Radio: “It could all have been avoided if Sue Gray had taken a salary of just slightly less than Keir Starmer, maybe a cut of £5,000 on what she’s taken…. The amount of difference that it would make in terms of her living standards is minuscule at that level.”

It came as a new survey by Opinium suggested the row is harming Sir Keir personally, with his net approval rating plummeting to -26.

A No 10 source said: “Whatever the noises off, this Government is completely focused on stabilising the economy and delivering the change Britain voted for. Nothing will distract us from that task.”

‘Jail Starmer’ graffiti probed

Meanwhile, police have also launched an investigation after graffiti saying “Jail Starmer” was daubed on the window of an MP’s office.

The Metropolitan Police said the graffiti was daubed on the window on Friday and they received an allegation of criminal damage a day later.

The words “Jail Starmer” in large white letters appeared at the south-east London office of Clive Efford, the Labour MP for Eltham and Chislehurst, according to images shown online by Sky News.

A police spokesman said: “On Saturday 21 September police received an allegation of criminal damage to an office building in Westmount Road, SE9.

“Graffiti had been daubed on the premises the previous day. An investigation has been launched and enquiries are ongoing.”