Britain’s most senior police officer has contradicted Theresa May’s claim that police cuts were not to blame for a rise in violent crime, as a renewed political focus fell on knife crime after two fatal stabbings of teenagers.

Cressida Dick said there was “some link” between violent crime on the streets and police numbers. The Metropolitan police commissioner was speaking on Tuesday after the prime minister sparked a backlash over the government’s handling of rising knife crime. May said there was “no direct correlation between certain crimes and police numbers” amid new evidence of a significant rise in teenagers using knives.

Dick said in an interview on LBC radio: “If you went back in history, you would see examples of when police officer numbers have gone down and crime has not necessarily risen at the same rate and in the same way.

“But I think that what we all agree on is that in the last few years police officer numbers have gone down a lot, there’s been a lot of other cuts in public services, there has been more demand for policing and therefore there must be something and I have consistently said that.”

The fatal stabbings of Jodie Chesney in an east London park on Friday night and Yousef Makki last week were discussed at a cabinet meeting on Tuesday, where May told ministers that their deaths were “a stark reminder that there is more to do to tackle violence on our streets”.

May tasked the Home Office with coordinating an urgent series of cabinet-level ministerial meetings and engagements to accelerate the work the government is doing in support of local councils and police, according to her spokesman.

Meetings will take place “as soon as possible” and were being treated as “a priority” by the prime minister, he added.

May also came under fire from the body that represents rank-and-file officers, which described her as “delusional”. John Apter, national chair of the Police Federation of England and Wales, said the stabbing deaths were “the true cost of austerity we warned of but were ridiculed for doing so”.

Mark Burns-Williamson, the chair of the Association of Police and Crime Commissioners, said cuts to police numbers nationwide and cuts to youth services had created “a toxic mix”.

There was also a call by Dick’s predecessor at Scotland Yard, Bernard Hogan-Howe, for 20,000 officers to be recruited to bring forces in England and Wales back to their 2010 strength as he demanded that ministers “get a grip on the crisis”.

Several MPs, including a former Home Office minister, have called for the government to convene a meeting of the Cobra emergency committee to respond to what the Birmingham Yardley Labour MP Jess Phillips described as a “national emergency”.

The home secretary, Sajid Javid, will chair a meeting of police chiefs on Wednesday that will bring together chief constables from the areas most affected by knife crime.

The prime minister was also accused by the mayor of London of crying “crocodile tears” over rates of knife crime.

Sadiq Khan blamed soaring levels of knife crime in the capital on police cuts, as well as cuts to youth and mental health services and schools.

Speaking to Sky News, he said: “We need much more resources from the government to invest in preventative services and policing. We have fewer police in London now in 2019 than at any time since 2003 – our population has grown by a million and a half since 2003.

“Also when it comes to youth services, over the last eight years, dozens and dozens of youth centres have closed down, hundreds of youth workers have lost their jobs, thousands of young people who used to have youth centres to go to [now] haven’t.”

Khan added: “We are doing our best to fill this hole, by ourselves though we can’t do it … Of course there’s a link between the number of police officers and crime going up, the Home Office themselves accept this.

“I’m not excusing criminality but there are complex reasons why violent crime has gone up, there are deep-seated social problems.”

He listed lack of opportunity, poverty, social alienation and mental health issues as some of the factors that have been exacerbated by cuts to services.

Dick, in the same interview on Tuesday, also suggested that middle class recreational drug users have “blood on their hands” over the recent spate of violent deaths.