Security has been increased at UK ports, border controls and a major railway station following the attack at the Paris office of magazine Charlie Hebdo, which left 12 people dead.
Armed and masked anti-terrorism police swooped on woodland villages northeast of Paris on Thursday in a manhunt for two brothers suspected of being the Islamist gunmen who killed 12 people at a French satirical weekly.
A day after the Paris attack, officers carried out house-to-house searches in the village of Corcy, a few km (miles) from a service station where police sources said the brothers were sighted in ski masks. Helicopters flew overhead.
The fugitive suspects are French-born sons of Algerian-born parents, both in their early 30s, and already under police surveillance. One was jailed for 18 months for trying to travel to Iraq a decade ago to fight as part of an Islamist cell. Police said they were “armed and dangerous”.
United States and European sources close to the investigation said on Thursday that one of the brothers, Said Kouachi, was in Yemen in 2011 for a number of months training with Al Qaeda in the Arabian Peninsula (AQAP), one of the group’s most active affiliates.
The UK terror threat level remains unchanged at “severe”, meaning a terrorist attack is “highly likely”.
BBC assistant political editor Norman Smith said an additional UK police officer had also been sent to join the UK’s existing counter-terror team in Paris.
There was no evidence the Paris terrorists had any ties to the UK, our correspondent added.
It comes after Mr Cameron offered France “any assistance our intelligence agencies can give” after the shootings, which killed eight journalists, two police officers, a maintenance worker and a visitor to the Charlie Hebdo office.
Dr Shuja Shafi, secretary general of the Muslim Council of Britain, also condemned the attack – believed to be in response to cartoons of the Prophet Muhammad.
“Nothing is more immoral, offensive and insulting against our beloved Prophet than such a callous act of murder,” he said.
A group of 15 UK imams released a statement saying “cold-blooded murder such as this is the antithesis of Islam and its tenets”.