The home secretary, Sajid Javid, has demanded cabinet colleagues sanction an emergency payment to police to help quell rising violence and is believed to have clashed with Theresa May over the issue in cabinet on Tuesday.

As the Labour leader, Jeremy Corbyn, blamed youth knife crime deaths on Tory funding cuts, two ministerial sources told the Guardian that Javid had clashed with the prime minister at cabinet.

His request for an emergency cash injection for the police to tackle knife crime was rebuffed by Philip Hammond, the chancellor.

May attracted widespread criticism for saying on Monday that police cuts she initiated while home secretary were not linked to rising violent crime, a claim Javid is understood to disagree with.

Police chiefs planned to ramp up the pressure at a meeting with Javid on Wednesday by asking for more money to deal with the issue, with one branding as “disgraceful” the prime minister’s claims that austerity-driven cuts had no link to rising violent crime.

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The meeting came as the London mayor, Sadiq Khan, demanded a special session of the government’s crisis committee, Cobra, be convened to stem the toll of stabbings.

In the letter seen by the Guardian, Khan said government leadership was failing, despite the home secretary setting up a serious violent crime taskforce which meets on Wednesday morning, which the mayor believes is too infrequent.

“Its failure to drive meaningful change across Whitehall was made clear on Sunday when the health secretary criticised public health approaches to tackling violent crime, despite this being current government policy,” he said.

“There is a precedent for the approach I am suggesting. Tony Blair, as prime minister, called a Cobra meeting on street crime in 2002 and continued to show personal leadership on the issue … This approach worked, with a 10% reduction in street robberies within six months.”

The prime minister’s problems were compounded on Tuesday when the Metropolitan police commissioner, Cressida Dick, publicly disagreed with May in a radio interview.

“In the last few years, police officer numbers have gone down a lot, there’s been a lot of other cuts in public services, [and] there has been more demand for policing,” she told LBC. “I agree that there is some link between violent crime on the streets obviously and police numbers, of course there is, and everybody would see that.”

Several other police chiefs told the Guardian that cuts to police and other public services had played a part, as did the Police Federation.

The Met said they had arrested “a male” in Leicester on Tuesday in connection with the murder of 17-year-old Jodie Chesney, who was stabbed in the back in a park in east London on Friday. Police said the male remained in custody awaiting transport to the capital, but gave no further details.

And police in Manchester charged two 17-year-olds, who cannot be named for legal reasons, over the death on Saturday of Yousef Ghaleb Makki, also 17. One was charged with Yousef’s murder and possession of a bladed article; the other was charged with assisting an offender and possession of a bladed article.

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Corbyn blamed the rise in violent crime on austerity. “Since 2010, we’ve seen 21,000 police officers taken off our streets and 760 youth centres closed,” he said. “We’ve experienced the tearing of the social fabric of our communities. Young people shouldn’t pay the price for austerity with their lives.”

At cabinet on Tuesday, Javid also asked for greater use of stop and search powers which was not met with approval by the prime minister, who scaled back the practice when she was home secretary.

Part of his argument was that black and ethnic minority children would be protected by such a move as they are more likely to be the victims of knife crime. One source said Javid appeared to have made the requests suspecting it would be turned down, but seemed to have been laying down a marker as the issue of violent crime could quickly turn toxic for the Conservative party if not dealt with.

On Wednesday, Javid is due to face police chiefs, including those from the seven worst-affected areas, who are likely to demand more resources.

The backlash after May said there was was “no direct correlation” between certain crimes and police numbers triggered an apparent U-turn from Downing Street on Tuesday.

Downing Street let it be known that the prime minister was trying to ramp up cross-government action and No 10’s spokesperson declined to repeat May’s controversial claims about the effect of cuts since 2010 which saw 20,000 officers lost.

Jon Boutcher, the chief constable of Bedfordshire and a former senior Scotland Yard counter-terrorism detective, told the Guardian: “There are so many links to the lack of police resources and the cuts in our public services that correlate to the rise in knife crime and other crime.

“There has been a loss of police officers on the streets and in schools that have a preventative effect and who capture intelligence from communities about potential offenders. While we have seen reductions in police resources, the policing mission has widened and we are expected to do far more with far less.”

Another police chief said: “What the PM said is disgraceful; of course there is a link between police numbers and the prevalence of this crime. Of course it makes a difference if there are thousands of officers less.”