Security in the UK has been increased, with more checks at Britain’s borders and more police officers deployed on the streets in response to Friday’s attacks by Islamic State jihadis in Paris, Theresa May has confirmed.

The home secretary will chair a Cobra meeting on Sunday to discuss the UK government’s response to the attacks in Paris, which resulted in the deaths of at least 129 people. Britain’s terror threat level remains “severe”, but David Cameron has said it will be reviewed.

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Speaking on the BBC’s Andrew Marr Show, May said: “As we find out more about what has happened in Paris, we will be looking to see if there are more lessons to be learned in the UK. There has been an increased police presence at some events, there will be greater searches of vehicles. People going through our ports will see a greater police and border-force presence and more searches of vehicles.”

Asked about reports that there are SAS officers on the streets of the UK, she said: “What we have done over the years since the Mumbai attack is to make sure that the police have the capability to deal with these incidents and there are tried and tested arrangements in place to give military support.”

She added: “British nationals have been caught up in this as well as French nationals. We stand absolutely shoulder to shoulder with the French in relation to this issue. I think we are both very clear that the terrorists will not win. We will defeat them.”

The attacks aimed at inflicting mass casualties have been seen as a sign the threat posed by Isis is “evolving”, and May said a review of the security response was taking place. “What we have seen from the attack in Paris was a coordinated attack, a planned attack on a larger scale,” she said.

The killings in Paris do appear to represent a change of tactic by Isis, which apparently caught French counter-terrorism officials by surprise.

Isis propaganda has led officials to fear “lone-wolf” attacks, possibly leading to small numbers of deaths or injuries, but the multiple and almost simultaneous attacks in Paris on Friday suggest large-scale planning and a strategic desire to inflict the kind of spectacular attack favoured by al-Qaida in the past.

Asked about the possibility of further action on the ground to defeat Isis in Syria, May indicated that the Conservatives would want Labour’s support in parliament before any authorisation. “If any further action needs to be taken there has to be a consensus. We have been very clear that we need this,” she said.

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Speaking on the same programme, Lord Falconer, the shadow justice minister, deflected questions on whether he or Labour would support further action against Isis in Syria.

Lord Carlile, the Lib Dem peer and the government’s former independent reviewer of terror legislation, said in an article in the Mail on Sunday that, in the light of the attacks, the government’s proposed new surveillance legislation should be introduced as quickly as possible.

“We don’t have time to wait. What is in the bill is for the most part pefrectly reasonable. it could pass through parliament within the next three to four weeks if the government decided that is what should happen and I believe that the necessary powers need to be on the statute book as quickly as that. It could have been London,” he later told Sky.

Hilary Benn, the shadow foreign secretary, confirmed his support for the bill. “It is important that the police and security services have the power they need to keep us safe. The debate is how we should balance that with our protection of privacy,” he said.