David Cameron has offered “thoughts and prayers” to the French people after at least 127 people were killed in Paris.
The British PM said he was “shocked” by the gun and bomb attacks, adding: “We will do whatever we can to help.”
The Foreign Office says it is “urgently investigating” whether any British nationals have been caught up in the shootings or hostage-taking.
There will be “strengthened policing at ports” and more police at public events in the coming days, UK police said.
Met Police Assistant Commissioner Mark Rowley, national policing lead for counter terrorism, called for “vigilance” from the public.
Downing Street said the prime minister would chair a meeting of the government’s Cobra emergency committee in the wake of the attacks.
Meanwhile, Sussex Police have confirmed Gatwick Airport’s North Terminal has been evacuated and they are dealing with a “suspicious package”.
People were shot dead at bars and restaurants at five other sites in Paris on Friday evening. Eight attackers are reported to have been killed.
Gunmen reportedly killed 80 people and took dozens hostage at the Bataclan concert hall, where US rock group Eagles of Death Metal were playing. The siege ended when security forces stormed the building.
Many public places in Paris have been closed in the wake of the attacks.
Transport to the French capital from the UK has been affected, with delays and fewer people choosing to travel:
- Eurostar passengers are being advised to arrive an hour early to St Pancras International due to expected delays.
- British Airways warns of delays to Paris flights due to extra security checks.
- Air France also says delays are expected following the “reinforcement” of border controls.
- Easyjet says flights are operating as normal, but passengers are asked to check their flights on the Flight Tracker page and to allow extra time for security checks.
- The airlines are offering a variety of options for passengers who do not wish to travel to Paris.
BBC News correspondent Richard Lister, reporting from outside St Pancras International, said a Eurostar train which would have been expected to hold 700 people left the terminal with just 200 on board.
The Football Association will hold talks with French counterparts on Saturday to discuss whether England’s friendly with France in London on Tuesday should go ahead.
The French national stadium, where France were playing Germany, was among the venues targeted by attackers on Friday.
The Lord Mayor’s Show in London is taking place as planned. Union flags are flying at half mast and the Lord Mayor led a two-minute silence at 11:00 GMT.
The City of London Corporation said Tower Bridge would be lit in the colours of the Tricolour from sundown on Saturday.
Flags are being flown at half mast at Downing Street.
A vigil is expected to be held in Trafalgar Square on Saturday evening.
French President Francois Hollande said the attacks were “act of war” organised by Islamic State militants, who have now claimed responsibility the attack.
President Hollande has declared a state of emergency and indicated he would tighten border controls.
Flowers have been laid outside the French Embassy in London and flags has been flown at half mast.
The French Embassy in the UK tweeted: “Ambassador Bermann: thanks @David_Cameron for your support on atrocious attacks. France knows it can always count on UK solidarity in crisis”
A Foreign Office statement said it was “very concerned” about the attacks, adding: “We are in close touch with the French authorities and are urgently investigating whether any British nationals are caught up in them.”
It said people with concerns about British relatives or friends in Paris should call
0207 008 0000.
Foreign Secretary Philip Hammond tweeted that he had “conveyed my condolences” to his French counterpart Laurent Fabius, adding that the UK “stands with France”.
The Prince of Wales has condemned the “bestial attacks” in Paris and said he wanted to express his “utter, total horror”.
Labour leader Jeremy Corbyn said the world needed to “look for peace” in the wake of the “horrific” attacks in Paris.
He said the atrocity was an attack on “all of us who stand for the kind of fair and inclusive societies we want to live in”.
Tweeting about the “deep tragedy”, Archbishop of Canterbury Justin Welby said: “We weep with those affected, pray for deliverance and justice.”
Scotland’s First Minister Nicola Sturgeon told BBC Radio Scotland: “France has had to bear more than what any country should be expected to over the course of this year, so this is awful beyond words.
“On behalf of the Scottish government, and I am sure this will be the case for governments across the world, we stand ready to help in any way that we can.”