Video report by ITV News National Editor Allegra Stratton
The Government is to introduce emergency legislation to make sure terrorists are not released automatically from prison halfway through their sentences.
Speaking in the wake of the latest terror attack in Streatham, Justice Secretary Robert Buckland also said the Parole Board should review cases before such offenders are freed.
The Streatham attacker, Sudesh Amman, had been living in a south London bail hostel near where he launched his attack following his recent early release from prison.
National Editor Allegra Stratton explains what this new terror emergency law means
Fanatic Amman was shot dead by police after grabbing a knife from a shop and attacking two bystanders in Streatham on Sunday.
A third person was injured by flying glass during the gunfire.
Speaking in the House of Commons on Monday, Justice Secretary Robert Buckland told MPs: "Yesterday's appalling incident makes the case plainly for immediate action."
Amman's attack comes two months after convicted terrorist Usman Khan embarked on a killing spree armed with two knives and wearing a fake suicide vest while attending a prisoner rehabilitation programme at Fishmongers' Hall near London Bridge, raising further questions over the release of terrorists from prison.
Mr Buckland told the House of Commons: "We cannot have the situation, as we saw tragically in yesterday's case, where an offender - a known risk to innocent members of the public - is released early by automatic process of law without any oversight by the Parole Board.
"We will be doing everything we can to protect the public, that is our primary duty.
"We face an unprecedented situation of severe gravity and, as such, it demands that the Government responds immediately and that this legislation will therefore also apply to serving prisoners."
Mr Buckland said offenders will not be considered for release until they have served two-thirds of their sentence and that no terrorists will be released before the end of their full custodial term unless the Parole Board agrees.
The Parole Board would be "strengthened" to deal more effectively with the risks that terrorists pose and steps would be taking to introduce the plans "as soon as possible", the MP added.
The Government will also consider making new legislation to ensure that extremists are more closely monitored on release and will review whether the current maximum sentences for terrorist offences are sufficient.
It's expected the emergency legislation could be brought in within two weeks and applied retrospectively so will apply to terrorists currently in jail.
ITV News Political Correspondent Paul Brand explains what the government proposals could mean:
Labour leader Jeremy Corbyn MP said he's uncertain "a law change is needed" and that the power of early release lies with the probation services.
He added: "There's certainly a need to examine what is happening within our prison system.
"It's under-staffed, and under-funded, and over-crowded."
However, the father of Jack Merritt who was killed in the Fishmongers' Hall attacks said longer sentences by themselves just was just "kicking the can down the road" and would give greater opportunities for prisoners to radicalise each other.
In a series of tweets, David Merritt said the "key has to be deradicalisation, rehabilitation, supervision & diverting people from this path in the first place".
"Shooting people dead on the streets after they have carried out attacks is the epitome of shutting the stable door after the horse has bolted; the ultimate failure of policy. That is no criticism of the police; they do their jobs admirably, but it shouldn’t have come to this."
Amman, 20, was back on the streets for just a few weeks before Sunday’s stabbing attack after serving half of his three-year and four-month sentence for possessing and distributing terrorist documents.
At the time, the court heard Amman had listed dying a martyr as one of his "life goals" and had posted al Qaida propaganda on a family WhatsApp group, exposing siblings as young as 11 to graphic material.
Amman's stash of manuals on bomb-making, knife-fighting and close combat included the titles Bloody Brazilian Knife Fighting and How To Make A Bomb In Your Kitchen.
After Amman was jailed, Alexis Boon, then head of the Metropolitan Police Counter Terrorism Command, said the then teenager had a "fierce interest in violence and martyrdom" and was fascinated with dying "in the name of terrorism,"
Adding the case was "a reminder of the need to be vigilant to signs of radicalisation and report it".
Ahead of the announcement in the Commons, Boris Johnson said the government is preparing to take action to end the automatic early release of prisoners currently in jail for terrorist offences.
The Prime Minister said de-radicalising people is a "very, very difficult thing to do", adding:
"There is a big psychological barrier, people find it hard to get back over, and that's why I stress the importance of the custodial option and that's why I have come to the end of my patience with the idea of automatic early release and I hope that people will understand why we're doing that.
"This is a liberal country, it is a tolerant country, but I think the idea of automatic early release for people who obviously continue to pose a threat to the public has come to the end of its useful life."
Last month, the Government also announced plans to introduce “polygraph tests” as part of a wave of measures being described as a “major overhaul” in the way terrorists are punished and monitored.
However, the idea has drawn criticism from some who disagree the style of testing, first seen in 1921, is accurate enough to determine if a subject is lying.
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On Monday, the Met police confirmed more details on the attack saying armed officers were following him as he left an address in Streatham shortly after 13:20pm.
Police understand Amman stole a knife, ran from a shop as he was pursued by a member of staff, and once outside attacked two members of public.
The Met confirmed the time from him entering the shop to beginning his attack outside was approximately 60 seconds.
Police say their officers responded, fatally shooting him within approximately 60 seconds of him beginning to attack people.
The three-storey building in Leigham Court Road where Amman had been staying remained cordoned off by police following the knife attack.
The Met’s Counter Terrorism Command also carried out dawn raids at two residential addresses in the south London and Bishop's Stortford areas as part of their investigation, but no arrest have been made.
Eye witness Dave Chawner was on his way to the cinema on Sunday afternoon when he ran towards the scene of what he believed was a mugging or shoplifting.
Instead he saw blood "all around" and a man "bleeding out" on the road apparently being stabbed by Amman.
"It was only when I heard what I thought was cars back firing, and then it happened multiple times that I realised it was something more," he told ITV News.
"Then I saw three plain clothed armed officers pointing their guns at the assailant on the ground and then we were told to get back and we turned around and saw behind me a bloke lying on the street bleeding out from the lower abdomen."
Mr Chawner told ITV News members of the public were "incredible" as they rallied around to help the victim.
"The public in general just knitted together and were incredibly calm and constructive but the fact the ambulance didn't arrive, people started getting angry."