Metropolitan Police Assistant Commissioner Neil Basu has said that Usman Khan was subject to an "extensive list of licence conditions" on his release from prison and that "to the best of my knowledge he was complying with those conditions".
Giving a statement outside Scotland Yard, Mr Basu said: "We know this attacker was attending an event called Learning Together and some of those present confronted this attacker to try and stop him."
Usman Khan killed a man and a woman in the knife rampage yesterday afternoon and injured three other people, who are being treated in hospital.
Earlier today, it emerged that the London Bridge attacker was a convicted terrorist released half-way through a 16-year prison sentence for a plot to bomb the London Stock Exchange.
The 28-year-old, who was on licence and wearing an electronic monitoring tag, was attending a conference on prisoner rehabilitation organised by University of Cambridge-associated Learning Together at Fishmongers' Hall and reportedly "threatened to blow up" the building.
Armed with two knives and wearing a fake suicide vest, Khan was tackled by members of the public, including ex-offenders, before he was shot dead by police on London Bridge next to the Hall.
Video footage posted online shows Khan being taken to the ground as one man sprays him with a fire extinguisher and another, reportedly a Polish chef, lunges towards him with a narwhal tusk believed to have been taken from the wall inside the Hall.
It is understood that Khan started "lashing out" in a downstairs room of the Hall but was grabbed by the conference-goers and bundled out of the front door as he tried to go upstairs.
British Prime Minister Boris Johnson visited the scene today with Home Secretary Priti Patel and Metropolitan Police Commissioner Cressida Dick.
Metropolitan Police Assistant Commissioner Neil Basu said Khan had been living in the Staffordshire area of England and that police were "not actively seeking anyone else" over the attack.
Police have been searching a three-storey block of flats in Wolverhampton Road, in Stafford, where Khan is believed to have lived.
In February 2012, Khan, who had been based in Stoke-on-Trent, was handed an open-ended indeterminate sentence for public protection over his part in an al Qaeda-inspired terror group that plotted to bomb the London Stock Exchange and build a terrorist training camp on land in Pakistan-controlled Kashmir owned by his family.
A list of other potential targets included the names and addresses of the Dean of St Paul's Cathedral in London, then London mayor Mr Johnson, two rabbis, and the American Embassy in London.
But the sentence for Khan, along with two co-conspirators, was quashed at the Court of Appeal in April 2013 and he was given a determinate 16-year jail term and freed on licence in December last year and made to wear the tag.
The Parole Board said it had no involvement in his release and that Khan "appears to have been released automatically on licence (as required by law), without ever being referred to the board".
Speaking before chairing a meeting of the Government's emergency committee Cobra last night, Mr Johnson said he had "long argued" that 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, that I think the public will want to see".
The attack came weeks after the UK's terrorism threat level was downgraded to "substantial" from "severe", meaning attacks were thought to be "likely" rather than "highly likely".
London Bridge was the scene of a terror attack in 2017 - also during a general election campaign - when eight victims were killed along with the three terrorists, who were also wearing fake suicide vests and armed with knives.