The Metropolitan police commissioner wants to increase the number of armed officers in London in the wake of the Paris attacks.

Sir Bernard Hogan-Howe said he expected to have to lose 5,000 of the capital’s 32,000 officers to cope with cuts likely to total £800m over four years after the spending review this month.

But he tried to reassure Londoners that the number of firearms officers was being reviewed as a result of the attacks in the French capital, in which 129 people were killed. He said the Metropolitan police was proud to be a mostly unarmed force, but the Paris attacks showed the need for change.

The commissioner told LBC radio: “I think what Paris showed us, with so many attackers, with so many scenes, moving around at speed ... we need to have a mobile reserve. And I’ve got a good idea how that can be achieved.”

He said he would announce the exact details of the plan in the coming weeks, but it would involve changes to the number of armed police. Currently, only about 2,000 officers are armed in London.

When asked whether that was enough, Hogan-Howe replied: “I think at the moment we’re fine. What I’ve said is ... we’re working on plans now so that in the short period of time, we’ve got an extra third on top of the core provision. The armed response vehicle element, we’re increasing by a third straight away. But then the overall pool I want to increase by a third overall and also at any one time, on duty, probably double.”

He went on to warn that terrorism should not alter the British way of life. Hogan-Howe said: “What we don’t want to do surely is kneejerk towards a new type of policing where everyone is armed. I think this type of attack shows the police have got to be ready, flexible and have enough reserves.”

The police operation at Tuesday night’s international friendly between England and France will involve some armed police officers, which he acknowledged would seem unusual to many.

The commissioner said: “I hope they’re reassured by it, not worried by it.” A few hundred officers would be protecting crowds, Hogan-Howe added. “We usually police football matches on the amount of football violence there might be there. We’re not expecting any tonight.”

He faced questions from listeners who suggested that all officers should be armed, but said overreacting would be giving the attackers exactly what they wanted. “What we should do is, we should think clearly about having more officers [being] better equipped and more available,” he said.

Hogan-Howe criticised an article by the Surrey police and crime commissioner, Kevin Hurley, which discussed the weaponry used by British police and warned that it was no match for the type of guns available to extremists. He said: “I think he’s been foolish to talk in great detail about our capability. Our officers need all the benefit of surprise we can achieve.”

The commissioner did not discuss any details of police techniques or equipment, but said the review would determine “whether or not we’re fit for purpose”. Hogan-Howe said his force had spent thousands on overtime in the wake of the Paris attacks and that it would “go into the millions” within weeks.

On the expected police cuts, he said: “If we could keep at least 30,000 cops, I can make this city safe. If it’s below that, I start to get worried.” There were between 3,000 and 4,000 extremists across the UK, including “very significant numbers” in London, Hogan-Howe said.

Authorities were more concerned about extremists who had travelled into the UK, rather than their homegrown counterparts, he claimed. “The ones we’ve got at home, on the whole, we believe that our security services have got a very good handle on them.”

Despite fears that militants could be exploiting the refugee crisis to move between countries undetected, Hogan-Howe said there had been no clear evidence of this occurring.