Ian Acheson, who carried out a review of the management of Islamist extremists in jail, said the prison service did not have the appetite or aptitude to manage terrorist offenders.
Their conditions are now not known.
Metropolitan Police Deputy Assistant Commissioner Lucy D'Orsi said he served time after being convicted of publishing graphic terrorist videos online and stockpiling instructions on bomb-making and knife attacks.
Sudesh Amman, jailed in 2018 for possession of terrorist documents and disseminating terrorist publications, was shot dead by police on Sunday after he went on the rampage with a stolen 25cm (10-inch) knife on a busy London street. Video from the scene appeared to show three undercover police officers in an unmarked auto making a quick stop and emerging with weapons.
The attack occurred in the Streatham neighbourhood of south London just after 2pm on Sunday (1am AEDT). They are truly the best of us.
However, police confirmed that the scene has now been fully contained.
"The incident was quickly declared as a terrorist incident", D'Orsi said, adding that the armed officers who shot Amman dead were part of a "proactive counter-terrorism surveillance operation".
Another woman, in her 20s, suffered minor injuries believed to have been caused by glass following the gunshots.
Sunday's attack was the second in less than three months by a recently released prisoner.
Prime Minister Boris Johnson praised police and emergency workers.
Prime Minister Boris Johnson had already promised changes following November's attack, with measures including forcing unsafe terrorists who receive extended determinate sentences to serve the whole time behind bars.
The Metropolitan Police have asked people to avoid the area as emergency services continue to deal with the incident.
"I heard two people got stabbed and apparently one man was shouting Allahu Akbar but people thought he was just a insane man, so he got away".
In November past year, in a similar scenario, two people were killed after convicted terrorist Usman Khan went on a stabbing frenzy in London Bridge area of the United Kingdom capital. "My thoughts are with the injured and all those affected", he said.
"But he didn't stop, and then I saw that they shot him three times".
"I think, looking at the problems we have with re-educating and reclaiming and rehabilitating people who succumb to Islamism, it's very, very hard, and very tough, and it can happen, but the instances of success are really very few", he confessed.
His words echo comments he made after London's last terror attack at Fishmongers' Hall near London Bridge when two people were killed by convicted terrorist Usman Khan. She said Streatham is a "wonderful community, extremely diverse and we haven't had an issue like this, as far back as I can remember and I've lived here my entire life".
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