Paris attacks: London landmarks lit in French colours
Major London landmarks have been lit in the colours of the French national flag in tribute to the 17 people killed in the Paris terror attacks.
Tower Bridge, Trafalgar Square and the National Gallery were among monuments lit in red, white and blue.
A huge unity march is taking place in Paris, while in the UK, crowds have taken over Trafalgar Square.
David Cameron, speaking in Paris, said it was "a day about people, about solidarity".
He told the BBC: "It was a demonstration of solidarity, people throughout this country, young and old, black and white, saying we stand with the victims.
"We are not going to put up with this because we are a free, open, tolerant country. As a Briton I felt that exactly the same."
Earlier he warned: "We in Britain face a very similar threat - a threat of fanatical extremism - and we have to confront that in every way we can."
Mr Cameron added he would be meeting security and intelligence chiefs on Monday to discuss whether further action should be taken to defend Britain against terrorist attacks.
Seventeen people were killed during three days of attacks in Paris which targeted satirical magazine Charlie Hebdo, police officers, and a kosher supermarket.
News agency AFP estimated that more than a million people attended the Paris rally on Sunday, which moved off from the Place de la Republique amid cheers, clapping and chants of "Liberte" and "Charlie" at 14:30 GMT.
Mr Cameron was among dozens of world leaders who linked arms at the head of the march, along with the victims' families.
In the UK, crowds gathered at Trafalgar Square in London and also in Leeds, Sheffield, Glasgow and Liverpool.
The BBC's Nick Eardley, at the scene in Trafalgar Square, said there were cheers as the French flag was projected onto the front of the National Gallery.
Tower Bridge was bathed in the colours of the French flag from 16:00, turning dark at 17:30. The emblem was also projected on to the National Gallery.
The Trafalgar Square fountains rotated the colours of the French flag, while the London Eye went dark, with the French colours projected on to County Hall behind it.
Elsewhere, a vigil was planned in Cardiff Bay in front of the Senedd which houses the Welsh government.
Sombre but defiant
By Nick Eardley, BBC News, at Trafalgar Square
There is a sombre but defiant mood as hundreds gather in London's Trafalgar Square to show support for the huge rally in Paris.
Among the crowd are many French expats and Britons offering their own messages of solidarity.
Many are holding signs that read Je suis Charlie, the words many have come to associate with French defiance in the face of extremism.
Others are holding similar signs saying Je suis Ahmed, a tribute to the Muslim police officer killed during the attacks on Charlie Hebdo's Paris office.
Some hold their pens and copies of cartoons aloft in support of free speech.
Avi Gelley, 29, is Jewish and lives in London. He spoke about how "scary" it was to see the attacks in France and said he feels "not safe at all" in London now.
But if we do not stand together against such attacks, he says, "it's only going to get worse".
Mathieu Gillet, 32, is from Paris and has lived in London for two years.
"I'm here to demonstrate that the three values of France - liberty, equality, fraternity - are still alive and we definitely have to fight for those values," he says.
"It's a strong message that people are standing shoulder to shoulder and together, from around the world."
London mayor Boris Johnson said he was "very pleased and proud that we've been able to show this gesture of solidarity and of unity with the people of Paris".
Labour leader Ed Miliband, also marching in Paris, said: "We've been inspired by the response of the French people, and indeed by the response of people across faiths, across communities, in this country."
French Ambassador to the UK Sylvie Bermann said she was grateful for the UK's show of solidarity, adding many people had signed books of condolence at the London embassy.
About 700,000 people were said to have taken part in marches across France on Saturday, including in Paris, Orleans, Nice, Pau, Toulouse and Nantes.
Sunday's Paris march was expected to dwarf these events and extra security was brought in to protect the marchers.
Other global figures attending include German Chancellor Angela Merkel, Italian Prime Minister Matteo Renzi, Russian Foreign Minister Sergei Lavrov and Nato Secretary General Jens Stoltenberg.
The offices of Charlie Hebdo were attacked by brothers Cherif and Said Kouachi, who went on the run but were later shot dead by police.
Eight journalists and two police officers were among the 12 people killed in that attack.
Another gunman, Amedy Coulibaly, took several hostages at a supermarket in eastern Paris, with four hostages found dead after the siege ended.
Coulibaly is also believed to be behind the killing of a policewoman in southern Paris on Thursday, and has been linked to the non-fatal shooting of a jogger on Wednesday.
Police are still hunting his partner, Hayat Boumeddiene - though she is now thought to have fled France last week and may be on her way to Syria.
How the attacks unfolded (all times GMT)
- Wednesday 7 January 10:30 - Two masked gunmen enter Charlie Hebdo offices, killing 12 people, including the magazine's editor. Shortly after the attack, the gunmen kill a police officer nearby.
- 11:00 - Police lose track of the men after they abandon their getaway car and hijack another vehicle. They are later identified as brothers Said and Cherif Kouachi.
- Thursday 8 January 08:45 -A lone gunman shoots dead a policewoman and injures a man in the south of Paris. Gunman later identified as Amedy Coulibaly.
- 10:30 - The Kouachi brothers rob a service station near Villers-Cotterets, in the Aisne region, but disappear again.
- Friday 9 January 08:30 - Police exchange gunfire with the Kouachi brothers during a car chase on the National 2 highway northeast of Paris.
- 10:00 - Police surround the brothers at an industrial building in at Dammartin-en-Goele, 35km (22 miles) from Paris.
- 12:15 - Coulibaly reappears and takes several people hostage at a kosher supermarket in eastern Paris. Heavily-armed police arrive and surround the store.
- 16:00 - Kouachi brothers come out of the warehouse, firing at police. They are both shot dead.
- 16:15 - Police storm the kosher supermarket in Paris, killing Coulibaly and rescuing 15 hostages. The bodies of four hostages are recovered.