The man shot dead by police following a stabbing attack is believed to be a convicted terrorist from Harrow who had recently been released from prison.
Police said the suspect was yet to be formally identified but they are "confident" he is 20-year-old Sudesh Amman.
It is understood that Amman, who was jailed for possessing and distributing terrorist documents in December 2018, had been freed in the past six weeks.
Amman, who at the time of his sentencing was 18 years old and had an address in Harrow, north-west London, had been jailed for three years and four months.
Sam Armstrong, from the Henry Jackson Society, said Amman was thought to have been staying in a bail hostel in Tulse Hill.
He said the society had warned in December that Amman was due for release within the next two months and should not be let out of prison.
Two people were stabbed in the attack in Streatham on Sunday afternoon which police believe to be "Islamist-related".
Scotland Yard said armed officers shot dead a man as part of a "proactive counter-terrorism operation" on Streatham High Road.
A device found strapped to the body of the suspect was a hoax, the Metropolitan Police added in a statement.
Three victims were taken to a south London hospital. One man, who is in his 40s, was initially considered to be in a life-threatening condition however, police say this is no longer the case.
A woman in her 50s had non-life threatening injuries and has been discharged from hospital.
Another woman in her 20s has minor injuries - believed to have been caused by glass following the discharge of the police firearm. She is still receiving treatment at hospital.
A Met Police statement added: "The situation has been contained and officers from the Met's Counter Terrorism Command are now leading an investigation into the incident.
"The incident was quickly declared as a terrorist incident and we believe it to be Islamist-related."
People took shelter in nearby shops as the incident unfolded on the busy south London high street.
Prime Minister Boris Johnson said he will announce plans on Monday for "fundamental changes to the system for dealing with those convicted of terrorism offences" following the attack.
He added: "Following the awful events at Fishmongers' Hall in December, we have moved quickly to introduce a package of measures to strengthen every element of our response to terrorism - including longer prison sentences and more money for the police."
On Sunday evening, forensics officers could be seen near Superdrug and Boots examining the area for clues.
Families could be heard asking police how they would be able to access their homes in light of the incident.
Streatham High Road remains closed with cordons in place, police said.
Stranded residents were being offered temporary accommodation inside the Odeon cinema in the cordon, with workers at Lambeth Council inside looking after those affected.
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