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
British Transport Police says London Bridge mainline station remains closed and Tube trains are not stopping at London Bridge Underground station.
It advises to check with Transport for London and National Rail before travelling.
Karen Bosch was travelling on a bus southbound over London Bridge when "it came to a sudden stop because there were people running across the road".
"It looked like there was a fight going on, there were people tussling with one each other and then I realised it was police wrestling with one tall, bearded man".
She told the BBC News Channel she heard "two loud pops and also saw a spent taser, and then the guy was lying on the floor.
"He then pulled his coat back which showed he had some sort of vest underneath... The police then moved backwards away quickly".
Former defence minister Tobias Ellwood, who came to the aid of a police officer stabbed outside Parliament in 2017, says this incident is a "stark reminder of the dangerous and diverse threats we continue to face" and praises emergency services.
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Image source, EPAA man has been detained and a number of people are believed to have been injured in an incident at London Bridge.
The Met Police say they were called to a stabbing at premises near the bridge in central London just before 14:00 GMT.
Scotland Yard says officers are "responding to this incident as though it is terror-related".
Videos on social media appear to show several people dressed in plain-clothes surrounding a man on the floor who then disperse before the man is shot by an armed police officer.
London Ambulance Service has declared a "major incident" and have a number of crews at the scene.
BBC Radio 5 Live
BBC Radio 5 Live has been speaking to eyewitness Dan Castleton, who was working nearby and was approaching London Bridge from the south side at around 14:05 GMT.
“We got to the bridge and a member of the public coming the other way fairly fast said, ‘don’t go that way, there's an incident’.
He began walking along the river towards, and within a few seconds heard a bang.
“There was about four or five more shots, that were obviously shots - people started to run a little bit faster away from it.
“Then there were a couple of louder bangs that seemed different - it might just have been the wind but it seemed as if they sounded different."
He said people did seem calm "but everyone was worried and nervous... lots of people were on their phones.
"I was a few minutes away from getting even closer, but fortunately I wasn't."
The prime minister is returning to No 10 from his constituency to receive further updates on the London Bridge incident.
The Met Police has urged people to use "common sense and restraint" when circulating pictures and videos of the London Bridge incident.
The force tweeted: "Help us keep you safe."
Find the latest information from police here, external.
Image source, PA Media
Image source, PA Media
Image source, PA MediaKing's College London says its Guy's Campus, situated close to London Bridge on the South Bank, has been "temporarily locked down".
The university tweets:
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At the scene, BBC home affairs correspondent Tom Symonds says the police have put in an "enormous cordon".
He said an officer warned him it was "a potential firearms incident" and told him to take "hard cover" if needed.
In its latest update, the Metropolitan Police said: "At this stage, the circumstances relating to the incident at London Bridge remain unclear.
"However, as a precaution, we are currently responding to this incident as though it is terror-related.
"One man has been shot by police.
"We will provide further information when possible."
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PA news agency is reporting that staff at Monument station claim five people have been injured in the incident.
The Tube station has been closed off as armed police investigate.
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Nurse Jackie Benfield, 32, has told the Press Association how she asked to be let off a bus on London Bridge after she heard "five or six" gunshots.
Ms Benfield, who was on her way home from work, said she exited the bus and "ran like hell" to escape the shots.
Connor Allen, who was in his van on the bridge when it was evacuated said: "Everyone just started running, you heard these pops and that was it.
"We just got out the van and started running."
Downing Street tweets...
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Priti Patel tweets...
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Image source, EPAA man has been detained and a number of people are believed to have been injured in an incident at London Bridge, police have said.
The Met Police said they were called to a stabbing at a premises near the bridge just before 14:00 GMT.
London Ambulance Service has declared a "major incident".
Eyewitnesses describe armed police arriving at the scene and shooting a man.
Videos on social media appear to show several people dressed in plain-clothes surrounding a man on the floor who then disperse before the man is shot by an armed police officer.
British Transport Police said London Bridge station was currently closed and no trains would be stopping there.
Details are still emerging of the incident, and we will be bringing them to you as soon as we can.
A white lorry was pictured across both lanes of the bridge.
Three police cars and a number of armed officers were seen near the vehicle.
It is not known if the lorry played any part in the incident.
Image source, ReutersA white lorry was pictured across both lanes on London Bridge