New specialist anti-terrorist response teams will be created in Birmingham, Manchester and other major cities to step up Britain’s ability to withstand attacks like those in Paris and Brussels, David Cameron has announced.

As he arrived in Washington for a nuclear security summit, hosted by Barack Obama, the prime minister said the government planned to create several teams in regions outside London that would be equipped to respond to potential terrorist attacks around the clock.

He also announced a series of other steps, including an increase of more than 1,000 in the number of armed police officers trained to operate on Britain’s streets by 2018, as well as the purchase of 40 additional armed police response vehicles.

The steps are the result of a review of armed policing ordered by Cameron last year in the wake of the attacks in Paris in which gunmen targeted a series of locations in the French capital on a single evening.

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Reports have suggested that the ringleader of the Paris attacks, and one of the suspects in the Brussels bombings, had both visited Birmingham. Steve McCabe, the Labour MP for Birmingham Selly Oak, had asked Theresa May what could be done to ensure that cities outside London were adequately protected.

Funding for the new measures will come from the £143m increase announced as part of the strategic security defence review to improve armed response capability, the government said.

The plans are intended to complement the military contingency planning set out by Cameron in the wake of the Charlie Hebdo attack in January last year, which would allow up to 10,000 troops to be deployed to protect the public in the event of an emergency.

Cameron said: “Our police and intelligence services work round the clock to keep us safe and it is absolutely vital that we support them with the right resources and kit. After the terrorist attacks in France last year, we decided to look at whether there was more we could do to protect people from the type of terrorist threat we now face. That’s why we are increasing the number of specially trained armed officers up and down the country to make sure the police have greater capability to respond swiftly and effectively should they need to do so.”

Simon Chesterman, the National Police Chiefs’ Council lead for armed policing, said: “Over recent years we have significantly enhanced the training, tactics and weaponry of armed officers to ensure that they are capable of dealing with all types of terrorist attacks. This additional uplift will ensure we are in an even stronger position to respond quickly and effectively to protect the public.”

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The total of new armed police officers includes 600 already announced in January. In 2014, when the last official figures were compiled, there were 5,875 armed police officers, though they were only deployed in strictly defined circumstances.

In the wake of the Brussels attacks, in which suicide bombers targeted the airport and the metro, May announced that extra armed officers were being posted on the transport system. However, the sharp increase in the number of armed officers now planned is also likely to underline fears that innocent bystanders could find themselves in the line of fire, as with the shooting of Jean Charles de Menezes in London in 2005, as the police scrambled to prevent what they feared was a planned suicide attack. De Menezes’s parents failed earlier this week in their attempt at the European court of human rights to challenge the decision not to prosecute the officers involved.

At the nuclear security summit in Washington, hosted by Obama and attended by more than 50 world leaders, the prime minister is due to discuss ways of protecting nuclear facilities from potential terrorist attacks, and ensuring that nuclear traffickers are dissuaded and apprehended.