One of the victims of Friday's attack is named as Jack Merritt, a Cambridge graduate
The condition of one of the victims in hospital has improved from critical to stable
A woman was also killed. Two further injured people remain in hospital
Usman Khan, 28, who carried out the attack, was a former prisoner convicted of terrorism offences
He was out on licence and wearing a tag. He was shot dead by police after people restrained him
Visiting the scene with London's mayor and the head of the Met Police, the PM says automatic early release from jail is not working
Police have been searching properties in Staffordshire
Friday's attack began during a conference at Fishmongers' Hall, near Monument, at 13:58 GMT
"We are also working at full tilt to understand exactly what has happened and whether anyone else was involved," says Met Police commissioner Cressida Dick.
"For this reason we expect cordons to remain in place around the London Bridge area for some time."
At a press conference, Met Police commissioner Cressida Dick says: "As well as the suspect who was shot dead by police, two of those injured in this attack in the London Bridge area have tragically lost their lives".
She also confirms that three people were injured in the attack.
Tom Symonds
Home Affairs Correspondent
What we don't know at this stage is what happened in the minutes before this group of passersby subdued this man and the police shot him.
We've had a good look at what the police are doing and it does look as though they are looking at areas some way away from the London Bridge station itself.
We have seen scene of crime officers in full forensic gear in masks around the Monument - north of London Bridge - and the tube station area.
They're also looking at a livery hall, the Fishmongers' Hall, which is next to the bridge.
Image source, Getty ImagesKhadir Meer, chief operating officer of London Ambulance Service, says: "We can confirm we took three people to two London hospitals following the incident at London Bridge today.
"We were called at 2:02pm and sent a number of ambulance crews and specialist response teams to the scene, including our hazardous area response unit and our tactical response unit.
"We declared a major incident and worked closely with other members of the emergency services at the scene.
"I would like to thank all our staff and the other emergency services who responded to this incident, including our medics at the scene, everyone in our control rooms and all those working hard behind the scenes.
"Our thoughts are with everyone who has been affected by what happened today."
Frank Gardner
BBC Security Correspondent
Wearing a fake explosive suicide vest might seem, on the surface, like an own goal.
But in fact it has two purposes in the minds of attackers: to add to public panic and also, in some cases, to ensure that police shoot the wearer dead.
To some attackers this 'martyrdom' is preferable to capture, trial and long years in prison.
Laura Kuenssberg
BBC political editor
Boris Johnson will convene a meeting of the government's emergency Cobra committee at 21:30 GMT.
Boris Johnson called the Labour leader Jeremy Corbyn tonight over the London Bridge attack.
The prime minister will receive further updates from security officials within the next hour to see what more has emerged.
Susan Hulme
Parliamentary correspondent
Image source, ReutersConservative Rishi Sunak joined other senior politicians in praising the emergency services
Leading party figures paid tribute to the emergency services involved in the attack at the start of the BBC's TV debate.
The Lib Dem leader, Jo Swinson, says everyone felt heartbroken by what they'd witnessed and the huge, huge courage shown by the public and emergency services.
The SNP leader, Nicola Sturgeon says there were exceptional acts of bravery on the part of the public.
Labour's Business spokesperson, Rebecca Long-Bailey, says: "I'm sure everyone's thoughts are with friends and families of those injured and two people we know have tragically died".
And the Chief Secretary to the Treasury, the Conservative, Rishi Sunak, pays tribute to the police for their "incredible bravery".
Image source, AFPPoliticians representing seven major political parties are appearing in a live BBC debate ahead of the general election in two weeks and so far, it's been dominated by the news from London Bridge.
"There's lots of early focus on London Bridge during this debate - and the first question is about how to tackle security issues," says our political correspondent Nick Eardley.
"Understandably, the tone so far is more discursive and there's little disagreement on supporting police to tackle security concerns."
Nick Eardley
Political correspondent
Prime Minister Boris Johnson has cancelled all political events tomorrow to focus on dealing with the aftermath of the London Bridge attack, Tory sources say.
BBC News Channel
Lloyd Griffiths filmed the second video in this clip from a bus on the bridge
Lloyd Griffiths filmed the attack from a bus as he headed north on London Bridge.
"It was kind of like an altercation at the start, or what looked like an altercation," he says.
"Most of us, we tried to stay calm. Nobody really knew what was happening. This was a really fast situation.
"Once we saw the person was shot by police we obviously knew that this was a really extreme situation.
"At that point we all went to the back of the bus, as far away as we could because the doors were locked.
"After about 30 seconds or so after that the police came across shouting, and telling us to get off the bus and run, and that's what everybody on the bus did."
Image source, EPAEvacuated residents in the London Bridge area, including those in King's College student accommodation, are being told to "prepare for the worst" by police.
Students Shohom and Ella, both 21, do not know when they will be allowed to return.
"We've been hearing from a lot of people on our WhatsApp group that we might have to stay out and that we won't be able to return to our residence tonight," says Shohom.
"The company that provides the accommodation is looking for alternative plans for the night. It's a bit of an inconvenience."
"But better safe than sorry," adds Ella.
Labour leader Jeremy Corbyn says his party will suspend campaigning in London tonight as a "mark of respect for those who suffered in this attack".
He says: "My heart goes out to the victims of this appalling attack.
"We owe a deep debt of gratitude to our police and emergency services, and the brave members of the public who put themselves in harm's way to protect others.
"We must remain united across all our communities, and we cannot let our democratic process be derailed by acts of terror."
BBC Radio 5 Live
Tour guide Stevie Hurst says he saw the suspect being held down and kicked him in the head.
"We saw a guy being accosted to the floor," he says, adding that people were "screaming" the attacker had "stabbed a couple of women."
"Everyone was just on top of him trying to bundle him to the ground," he says.
"We saw that the knife was still in his hand... I just put a foot in to try and kick him in the head.
"We were trying to do as much as we could to try and dislodge the knife from his hand so he wouldn't harm anyone else."
London Bridge mainline station has re-opened, National Rail says, external.
But check its site as some trains might be delayed, cancelled, or revised.
Image source, AFPThe London Fire Brigade has just released an update.
Assistant commissioner Andy Roe says: “We train alongside our emergency service partners to be ready for this kind of emergency and will continue to remain alert and prepared to respond.
"At the height of the incident, and in addition to the specially trained officers attending, six fire engines, a command unit and 30 firefighters were positioned at the scene to assist.
“Our thoughts today are with all of those affected by the terrorist incident at London Bridge."
Image source, PA Media"A police officer came up to me and said 'turn off your engine, get out and run'."
Mustafa Salih was behind the wheel of a bus heading towards London Bridge when he was ordered to join the crowds fleeing a sudden violent attack at one of the city's most well-known locations.
That was the moment he realised the bridge had been targeted for the second time in three years.
Mr Salih, 62, was travelling from Borough High Street when he saw a stream of people, including some in tears, running towards him.
British Transport Police tweet, external: "We are working with @networkrail to reopen London Bridge station, including the Underground.
"Some exits will remain closed as a result of the earlier terror incident. Officers remain on scene supporting @metpoliceuk and @CityPolice."
A Tory source has told the BBC's Laura Kuenssberg that the Conservatives are suspending general election campaigning in London for the night.
Two members of the public have been killed, as well as the attacker, Whitehall sources say.