Amber Rudd dismissed claims on Sunday that police cuts were to blame for the rise in violent crime as she prepared to publish a new strategy to tackle the problem.

The home secretary insisted that police forces across the country had the resources and the manpower to tackle the increasing violence on Britain’s streets.

“While I understand that police are facing emerging threats and new pressures, leading us to increase total investment in policing, the evidence does not bear out claims that resources are to blame for rising violence,” she said.

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The shadow education secretary, Angela Rayner, said Rudd was sticking her head in the sand and naive to suggest that the reduction in police numbers was not a factor.

Her comments come after a week in which nine people were stabbed to death in London, taking the number killed in violent attacks since the start of the year to more than 50. In the latest incident, a man was stabbed outside a Tube station on Saturday night.

Rudd will publish a new strategy on tackling serious violence on Monday. It will include an offensive weapons bill with new laws to restrict the carrying of knives and acid,and more severe punishment for those who carry weapons. It will also include measures to tackle violence through social media and in schools.

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A taskforce will be set up, bringing together ministers, councils, police commissioners and health and education experts, and Rudd will appeal to her critics to join her in tackling the problem: “The time for political quarrels is over. It is the time for action,” she will say.

The communities secretary, Sajid Javid, backed tRudd, saying the evidence did not suggest that police cuts were responsible for rising violent crime. He told the BBC: “We had much higher numbers of police 10 years ago and much higher numbers of violent crime.”

The policing minister Nick Hurd initially appeared to cloud the issue when he admitted that the police were stretched, but then added that it was “categorically not the case” that cuts had led to the rise in violent crime.

The Labour leader, Jeremy Corbyn, tweeted:

Jeremy Corbyn (@jeremycorbyn) .@Theresa_May and @AmberRuddHR are ignoring their record on security. They have cut 21,000 police officers from our streets. pic.twitter.com/JbIkVCBerK

Writing in the Sunday Telegraph, Rudd said that when knife crime was soaring in 2008, police numbers were close to the highest they had been in decades. She said police funding had been protected, and that most forces had reserves they could rely on, including the Metropolitan police which has £240m if needed.

Rayner told the BBC: “It’s not just about austerity but I think when the home secretary sticks her head in the sand and suggests that losing 21,000 police officers off our streets doesn’t have an effect then I think that’s a very naive position.”

Rayner also said cuts to youth services and education had had a knock-on effect: “It’s not just about police, of course it’s not, it’s about the wider public service and supporting families to make the right choices.”

Home Office statistics show the number of police officers fell from 143,734 in March 2010 to 123,142 in March 2017.

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Rudd defended stop-and-search as a vital policing tool in response to a row over whether the government should increase its use to tackle serious violence. Javid confirmed ministers would consult on the issue. “We will listen and if we need to extend those powers that is exactly what we will do,” he said.

Rayner said Labour supported evidence-based stop-and-search tactics based on local intelligence so that young people were not targeted based on their ethnicity. “It’s targeting stop-and-search rather than just going randomly around saying ‘I think you look like you might be a gang member so therefore I’m going to stop and search you’,” she said.

The Met has deployed an extra 300 officers this weekend, and the mayor of London, Sadiq Khan, is holding a meeting of London MPs, council leaders at City Hall and the Met commissioner, Cressida Dick, on Tuesday.