The man who carried out Friday's stabbing attack at London Bridge was a former prisoner convicted of terrorism offences.
The attacker, named by police as 28-year-old Usman Khan, was out of prison on licence at the time of the attack, in which a man and a woman were killed and three others were injured.
Khan was shot dead by officers after members of the public restrained him.
Police declared the attack a terrorist incident.
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.
The Times reported that Khan's release from prison last year came after he agreed to wear an electronic tag and have his movements monitored.
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."
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.
The suspect had been attending the event, where dozens of people - including students and former prisoners - were present, the BBC reports.
Mr Basu said the attack is understood to have started inside the building before proceeding onto London Bridge itself, where Khan was confronted and shot by armed officers.
The Met Police is stepping up patrols and cordons will remain in place. It is urging the public to continue to avoid the area and is asking anyone with information that could assist the investigation to contact them.
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. 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 actions of the public have been widely praised, including by Prime Minister Boris Johnson, Labour leader Jeremy Corbyn and Ms Dick, who said they had shown "extreme courage".
Videos posted on social media on Friday appeared to show passers-by holding Khan down, while a man in a suit could be seen running from him, having apparently retrieved a large knife.
One witness described how a man at the event 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.
Earlier, Mr Basu said Khan was wearing what was believed to be a hoax explosive device.
BBC security correspondent Frank Gardner said attackers wear fake suicide vests to add to public panic and, in some cases, to ensure police shoot them dead.
To some attackers, martyrdom is preferable to capture, trial and spending many years in prison, our correspondent added.
The prime minister, who has returned to Downing Street from his constituency, convened a meeting of the government's emergency Cobra committee.
He praised the emergency services and witnesses who intervened, and said he had "long argued that it is a mistake to allow serious and violent criminals to come out of prison early".
London Mayor Sadiq Khan thanked the members of the public who showed "breathtaking heroism" in running towards danger - "not knowing what confronted them".
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