BBC reported that the alleged attacker was under active police surveillance at the time of the incident, which police believe to be "Islamist-related".
The latest confirmation came hours after the man was killed by police in a "terror-related" incident where at least three people were injured, one of them being in a life-threatening condition, Xinhua news agency reported.
Metropolitan Police confirmed that armed police shot a male suspect on Streatham High Road at around 2 p.m. (1400GMT) as part of a "proactive counter-terrorism operation".
Local media reports suggested that the man entered a shop and started stabbing people. Police said the man had a hoax device strapped to his body.
Witnesses were quoted as saying they heard three gunshots and saw a man lying on the ground outside a Boots pharmacy, as armed police approached and shouted at those nearby to move back.
British Prime Minister Boris Johnson thanked the emergency services on his twitter account, saying that his thoughts are with the injured and all those affected.
Johnson's government pledged earlier this year that terror offenders will face more time in jail and be monitored more closely as part of new laws being introduced in the post-Brexit era.
Britain has been familiar with terror-related attacks over the past years.
In November, two people were stabbed to death when a convicted terrorist launched a frenzied knife attack in central London.
( With inputs from IANS )