British authorities have named the suspect who was shot dead by police after a stabbing spree that left two members of the public dead, with three in hospital.
The Met Police has declared the attack a terrorist incident.
The suspect, who died at the scene, was believed to have been wearing a hoax explosive device, police said.
Police named the suspect as 28-year-old Usman Khan, who was out of prison on licence at the time of the attack.
Khan was known to the authorities, having been convicted for terrorism offences in 2012, according to Met Police Assistant Commissioner Neil Basu.
"He was released from prison in December 2018 on licence and clearly, a key line of enquiry now is to establish how he came to carry out this attack," he said in a statement.
Officers are carrying out searches at an address in Staffordshire, where Khan had been living.
"Whilst we are still in the early stages of the investigation, at this time we are not actively seeking anyone else in relation to the attack," he added.
"However, we continue to make fast time enquiries to ensure that no other people were involved in this attack and that there is no outstanding threat to the public."
A man and a woman killed
A man and a woman were killed during the attack, Mr Basu confirmed. Three others - a man and two women - were also injured and remained in hospital in the early hours of Saturday morning (UK time). None has so far been named.
Officers were still working to identify those who were killed, Met Commissioner Cressida Dick said on Friday.
Simon Stevens, head of the NHS, said on Friday that one was in a critical but stable condition, another was stable and the third had less serious injuries.
The attack began at 13:58 GMT on Friday at Fishmongers' Hall, at the north end of London Bridge, where a Cambridge University conference on prisoner rehabilitation - called Learning Together - was taking place.
One witness described how a man at Fishmongers' Hall grabbed a narwhal tusk - a long white horn that protrudes from the porpoise - that was on the wall and went outside to confront the attacker.
The suspect had been attending the event. He was released from jail a year ago on agreeing to wear an electronic tag and have his movements monitored, according to The Times.
Dozens of people were at the event, including students from the university and former prisoners.
Videos on social media appeared to showed passers-by holding down a man. An officer arrives, seems to indicate to the group to move, and fires a shot.
A Whitehall source confirmed to the BBC two members of the public had died but gave no further information.
Mr Basu, head of UK counter-terrorism policing, said the force was keeping an open mind over the motive.
He said officers were called to a stabbing at a premises near the bridge just before 2pm.
"A male suspect was shot by specialist armed officers from City of London police and I can confirm that this suspect died at the scene," Mr Basu told a press conference.
He sad a "wide cordon remains in place" following the incident.
"Officers continue to carry out extensive searches in the area to ensure there is no further threat to the public."
BBC Security Correspondent Gordon Corera quoted sources saying there was no intelligence of anything about to happen, and police reacted to events as they unfolded.
The UK threat level was lowered from severe to substantial at the start of November, reflecting an assessment from the Joint Terrorism Analysis Centre that an attack was likely rather than highly likely because of a relative decline in activity.
In the wake of previous incidents in both the UK and other countries, police have been prepared for this kind of incident and seem to have been fast to intervene in this case, taking few chances, although members of the public were also involved in restraining the individual, Corera wrote.
Witnesses describe police response
Amanda Hunter, who was on a bus on London Bridge at the time, said: "All of a sudden [it] stopped and there was some commotion and I looked out the window and I just saw these three police officers going over to a man.
"It seemed like there was something in his hand, I'm not 100 percenbt sure. But then one of the police officers shot him."
Bus driver Mustafa Salih, 62, was travelling from Borough High Street towards London Bridge where he saw emergency vehicles and the police cordon.
He told BBC London: "A police officer came up to me and said 'turn off your engine, get off and run'.
"I looked up and I could see a crowd of people coming towards me.
"One woman was crying. I ran back down to Borough High Street. It was all very scary as we did not know what was happening."
Prime Minister Boris Johnson, who returned to Downing Street from his constituency, said the emergency services and members of the public who intervened "represent the very best of our country".
"This country will never be cowed or divided or intimidated by this sort of attack and our values, our British values, will prevail," he said.
British Prime Minister Boris Johnson told ITV News it was important to enforce terrorism-related sentences.
"It is a mistake to allow serious and violent criminals to come out of prison early and it is very important that we get out of that habit and that we enforce the appropriate sentences for dangerous criminals, especially for terrorists," Mr Johnson said.
Britons head to the polls on 12 December to elect a new government. The Conservative and Labour parties both said they had suspended election campaigning for the night following the attack.
London Mayor Sadiq Khan thanked the members of the public who showed "breathtaking heroism" in running towards danger - "not knowing what confronted them".
The Independent Office for Police Conduct said it has begun a mandatory investigation into the shooting.
London Bridge station and Tube reopened after it was earlier closed, Network Rail said, but warned trains may continue to be delayed, cancelled or revised as services were reinstated.
In a separate incident, Dutch police have since reported several people injured after a stabbing attack on a shopping street in The Hague.
Read about how the events unfolded: