The prime minister has sparked a backlash over the government’s handling of rising knife crime after she insisted there was “no direct correlation between certain crimes and police numbers” amid new evidence of a significant rise in teens using knives.

Police and crime commissioners, senior officers and youth workers pushed back against Theresa May’s comments as a political row erupted over the government’s grip on knife crime.

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

Labour called the rising death toll from stabbings a national tragedy and attacked what it claimed was a lack of leadership by May, who promised “a cross-government response”, with the home secretary meeting chief constables on Wednesday to discuss the problem.

Play Video 0:34 No link between knife crime and police cuts, claims Theresa May – video

New police figures released under the Freedom of Information Act for a Channel 4 documentary on Monday showed a 53% increase in the number of teens using knives for robberies, murders and rapes or sexual assaults between 2016 and 2018. The number of children under 16 being treated for blade wounds almost doubled in the last five years, NHS data has shown.

Speaking during a visit to Salisbury on the anniversary of the novichok attack on Sergei and Yulia Skripal, May said: “If you look at the figures, you’ll see there’s no correlation between certain crimes and police numbers.

“What matters is that police are responding to these criminal acts when they take place, that people are brought to justice, but what also matters is as a government we look at the issues that underpin this use of knives and that we act on those.”

On Monday, pupils at Manchester grammar school held a two-minute silence to remember the latest victim, Yousef Makki, a 17-year-old A-level student at the school who was stabbed to death on Saturday in a village near Altrincham. Two 17-year-old boys have been arrested on suspicion of his murder and remain in custody. On Monday night, detectives were granted another 24 hours to question them.

In London, murder detectives continued to investigate the stabbing of 17-year-old Jodie Chesney on Friday. Chesney was killed while sitting in a Romford park listening to music with friends. The suspect was described by police as “a black male in his late teens”.

Scotland Yard said it had experienced “a tragic 10 days” in the capital, involving two non-fatal stabbings in the West End on Sunday, fatal stabbings in Hendon and Ilford and an attempted murder in Enfield.

The Metropolitan police deputy assistant commissioner, Graham McNulty, said police shifts have been extended to try and counter the knife threat in the capital, but warned: “I can’t magic officers out of thin air.” He added that available staff were already “working incredibly hard in difficult circumstances”.

Burns-Williamson added: “If we had more police officers and resources, which have been cut over the last eight to nine years, we would be in a better position. I wouldn’t put it all down to police numbers, but police forces across the country are struggling to meet the demands of this kind of violent crime.”

He said reductions in neighbourhood policing meant there was now less police engagement with young people, adding that “austerity has absolutely played into some of this”.

“More needs to be done to ensure sustained support and funding for our policing, youth services and wider prevention services,” he added.

The home secretary, Sajid Javid, later defended the government’s record and told the Commons that knife crime was “a huge priority across government”.

“I really wish standing here there was just one simple answer, one single thing that could be done,” Javid told MPs. “We require action across multiple fronts and the best way to achieve that is for all of us to recognise that and to work together to deliver it.”

Javid said a new bill on offensive weapons was passing through parliament and the government wanted to give police greater confidence to stop and search people.

The recent spate of killings have fuelled concern that the use of knives is becoming normalised in society, partly through social media, and that stretched police and youth forces are struggling to reverse that trend.

In the West Midlands, where three teenage boys were stabbed to death in the last 10 days, the police and crime commissioner, David Jamieson, said “the swagger is back” among criminals, whose confidence has grown following the reduction of 2,000 police officers in the force in the last eight years.

“Some of these people think they can get away with it,” he said. “It’s a national emergency. If we don’t stem this now, we are going to see it increase.”

“It is no longer the stereotypical black lad from the flats,” said Raymond Douglas, a youth worker and founder of the Gangology initiative in Birmingham. “Historically, Liverpool, Manchester and Birmingham have been on the radar, but now I am finding myself in places like Swindon, Wigan and Portsmouth, talking to young white men.”

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He said that violence is a theme that runs through youth culture, citing trap music, video games and language as ways it is normalised. He highlighted other structural problems, including the way schools handle exclusions and deep cuts to services like youth clubs which he described as “places you can resolve conflict”.

But he said it would be wrong for the country to react more quickly to the deaths of white and middle-class children. “Whether they are from the 17th floor of the tower block or a leafy suburb, they are all our children and have to be treated the same way,” he said.

Dame Louise Casey, the former director of the Cameron government’s troubled families unit, said it “defies logic” to say police numbers weren’t affecting the issue, but stressed the impact of other cuts too in making prevention harder.

“There’s a deprivation and poverty issue that underpins this,” she said. “This is largely happening to poor people where we have shut children’s centres and Sure Start centres. In some of these areas, I have never seen so few preventative resources.”