Islamic State's propaganda arm claimed responsibility for the attack Monday, referring to Amman as a "fighter".
One of the three stabbing victims is being treated for life-threatening injuries.
"It is time to take action to ensure, irrespective of the law we are bringing in, people in the current stream don't qualify automatically for early release".
Johnson said deradicalisation and rehabilitation were hard and the instances of success were few.
"The suspect had been recently released from prison where he had been serving a sentence for Islamist-related terrorism offences", D'Orsi said of Sunday's attacker.
DAC D'Orsi clarified in her statement that the armed police officers shot the suspect dead immediately.
Amman reportedly pleaded guilty to six counts of possessing material useful for terrorism and seven counts of disseminating material on Skype between April 19, 2017, and April 2, 2018, on the basis of recklessness.
Sky News cited security sources as saying the incident was related to Islamist militancy.
Streatham Member of Parliament Bell Ribeiro-Addy told CNN that the attack in her constituency is "very sad and also quite scary".
Britain has about 220 people in prison with terrorism convictions.
"The circumstances are being assessed", the Metropolitan Police tweeted.
The knife-wielding terrorist who was shot dead in London has been named as Sudesh Amman - a man who was recently released from jail after being convicted of 13 terror offences in 2018.
Amman, 20, was released in January, but was deemed sufficiently high risk so he has been under special monitoring by police ever since.
Another eye-witness who gave first aid to one of the victims told LBC radio he heard what he thought was a vehicle backfiring, then two, possibly three armed police officers.
Metropolitan Police have urged people to avoid the area and London Ambulance Service said they had a "number of resources" at the scene.
Police said in a statement that a hoax device was found strapped to the body of the man killed by armed officers. A spokesman for IS said the group was also calling for the sabotage of a peace plan proposed by US President Donald Trump to resolve the Israeli-Palestinian conflict.
They were tipped off about him by a Dutch blogger, who noticed him on the encrypted Telegram app, where he used the moniker @strangertothisworld. "Or do you disperse and try to stop them reinfecting each other?"
He was 17 and living at home with his mother and younger siblings when he first began committing terrorism offences, according to authorities.
Messages showed that he had discussed with his family, friends and girlfriend his extreme views and desire to carry out an attack, often focused on using a knife.