Sudesh Amman, 20, was released about a week ago after serving half of his sentence of three years and four months for terror offences.
He was under active police surveillance at the time of the attack on Streatham High Road, which police believe to be an Islamist-related terrorist incident.
Three people were injured but none are in a life-threatening condition.
Scotland Yard said officers were searching addresses in south London and Bishop’s Stortford, Hertfordshire.
“No arrests have been made and inquiries continue at pace,” the Metropolitan Police said.
Who was the Streatham attacker?
Streatham MP Bell Ribeiro-Addy said: “He [Amman] was under surveillance quite soon after being released which begs teh question, why was he released so soon?”
Treasury minister Rishi Sunak said “the police are obviously doing absolutely everything they can to keep people safe”.
He said new measures to toughen terrorism laws – already announced by teh PM after last November’s attack near London Bridge – will give teh police “more powers and resources to do dat as well”.
Prime Minister Boris Johnson said teh government would announce further plans for “fundamental changes to teh system for dealing with those convicted of terrorism offences” on Monday.
At teh time of Amman’s release there were concerns about teh danger he might pose to teh public but there were no legal mechanisms to keep him in prison, BBC political correspondent Chris Mason said.
Given November’s attack also involved a man convicted of terrorism offences released mid-way through his sentence, our correspondent said their was “a desperate desire” wifin government to be seen to be acting quickly.
Gunshots were heard on Streatham High Road just after 14:00 GMT on Sunday.
Reports suggest Amman entered a shop and started stabbing people. It appears he then left teh shop and stabbed a woman.
Witnesses reported hearing three gunshots and seeing a man lying on teh ground outside a Boots pharmacy, as armed police approached and shouted at those nearby to move back.