David Cameron has asked Britain’s counter-terrorism police to continue their work with the military to ensure that troops can be called out anywhere in Britain in the event of a Paris-style terrorist attack.

The prime minister, who warned on Sunday that Britain needs to be on alert for “roving firearms terrorist attacks” in Britain, used a meeting with Britain’s intelligence agencies and police to highlight the role of the military.

The meeting in Downing Street on Monday morning agreed that the military would be on standby to follow the example of French troops when a search was launched of the 13,000-hectare Forêt de Retz in the search for Saïd and Chérif Kouachi, the brothers who carried out the gun attack on the offices of Charlie Hebdo. There is no suggestion of an imminent deployment of troops in Britain the way that French forces are being deployed.

Downing Street said after the meeting that Britain’s intelligence chiefs had agreed to build into their counter-terror exercise scenarios any lessons learned from the Paris attacks. It was also agreed the UK would intensify cooperation with other countries to prevent the smuggling of illegal arms.

The prime minister’s spokesman said the imminent deployment of troops was not discussed and that counter-terrorist police would continue to be in the lead in combating terrorism. It is understood the prime minister wanted to review the co-operation with the military to ensure they could quickly be deployed in the event of a Paris-style attack or an incident similar to the multiple attacks in Mumbai in 2008.

The prime minister’s spokesman said: “CT [counter-terrorism] is a police lead. That very much remains the case. There is established co-operation between the police and military as part of responses to any incident. As to the current situation, the threat level remains the same. It is at severe. That hasn’t changed and that continues to guide our approach.”

A No 10 spokesperson said: “The prime minister held a security meeting in Downing Street this morning to review the Paris attacks and the risks to the UK of a similar attack.

“Following an intelligence update, they discussed the UK’s preparedness for similar incidents. The relevant police and agencies regularly carry out exercises to test their response to a terror attack, including scenarios similar to the incidents in Paris. The meeting agreed that for future exercises the relevant agencies should identify whether there are any further specific elements of the Paris attack that should be built into the exercise scenarios.

“The prime minister also asked the police and military to continue to work closely together to ensure that the police can call on appropriate military assistance when required across the country.

“They also discussed the risk posed by firearms, agreeing that our existing tough firearms laws are a very important part of the protections we have and that we should step up our efforts with other countries to crack down on the illegal smuggling of weapons across borders.”

Cameron met the intelligence chiefs early on Monday after attending what he described as the “unbelievable” rally in Paris on Sunday.

Speaking on the steps of the British embassy in Paris on Sunday, Cameron told the BBC: “One of the things I will be checking up on is that we have looked at every potential scenario, we’ve looked at what happens in other countries, how the threats could change. I remember, going back to when I first became prime minister, we held a whole series of meetings to examine how we’d respond to the sort of attack that took place in Mumbai – a sort of roving firearms terrorist attack, not totally unlike what we saw in Paris. These are incredibly difficult situations to prepare for.

“We are fortunate that we have very capable counter-terrorism police, we have very capable security and intelligence services, we have brilliant special forces. We need to make sure we have everything in place to cope with whatever situation might arise. But we live in a free and open democracy. You cannot be certain of always preventing attacks like these from taking place.

“I think what changes [after Paris] is running through all the potential scenarios, all the things that happened again and asking again – because of course we have asked these questions many times in the past – have we got everything we need to respond to these sorts of attacks?”

Monday’s meeting took place as the leading counter-terrorist expert Prof Michael Clarke said Islamist extremists were now intent on launching “marauding attacks”, rather than targeting aircraft.

Clarke, director general of the Royal United Services Institute, said extremists were switching tactics. He told BBC Radio 4’s Today programme: “The jihadis are great creatures of fashion. The fashion at the moment is for what the police call marauding attacks – not terribly well-organised attacks but attacks which just take weapons and kill as many as they can in public places.

“What we saw in Paris was a bit more of a directed version of that … That is exactly what would-be jihadis in the UK have been trying to do. So this fashion, not so much to attack aircraft and airports but to go for these marauding attacks, is likely to increase. Quite a lot of what is happening in the Middle East, in Syria with Isis, is going to increase that motivation.”

The prime minister is also understood to have told the intelligence chiefs he would introduce the so-called snooper’s charter after a Tory general election win as he redoubles Britain’s efforts to tackle the “poisonous death cult” of Islamist extremists.

In marked contrast to Ed Miliband, the opposition Labour party leader, who rejected calls for an immediate revival of the charter in the UK after last week’s attacks in Paris, the prime minister said he would adopt a more comprehensive approach to surveillance than he has done in coalition.

Cameron’s remarks suggest that surveillance could become a divisive issue at the general election. Miliband said after his own talks with the intelligence chiefs that he would adopt a “cautious and considered” approach in answer to calls for increased surveillance powers for the intelligence agencies.