Britain is to urgently overhaul the law regarding convicted terrorists after police shot dead an extremist on early release from prison who stabbed two people in an attack claimed by the so-called Islamic State group.

Justice Secretary Robert Buckland promised to introduce "emergency legislation" to end the current arrangement whereby terrorist offenders are released automatically after they have served half of their sentence.

Any early release would be subject to a risk assessment from the Parole Board, he said, adding the new measures would apply to serving prisoners.

"The earliest point at which the offenders will now be considered for release will be once they have served two-thirds of their sentence," he told MPs.

Mr Buckland was speaking after Sudesh Amman, who was wearing a fake suicide vest, was shot dead after knifing two people on a busy street in Streatham, south London.

The IS propaganda arm called Amman "an IS fighter" and said "he carried out the attack in response to a call to target nationals" of countries belonging to the global coalition fighting against the jihadist group.

Amman was freed last week from prison after serving part of his sentence for 16 Islamist-related terror offences - namely the possession and distribution of terrorist documents, Mr Buckland said.

The attack came just over two months after a similar incident when armed police shot dead a convicted terrorist on early release near London Bridge in the heart of the city.

Usman Khan stabbed two people to death after attending a prisoner rehabilitation conference.

Prime Minister Boris Johnson questioned why Amman was released automatically with no involvement from the Parole Board and raised concerns about the effectiveness of de-radicalisation programmes in and out of jail.

"My anxiety is that we do not want to get back to a system where you have a lot of very, very laborious surveillance by our hard-pushed security services... when a custodial version might be better," he told reporters.

Previous measures announced after the London Bridge attack included tougher sentences of at least 14 years for the most serious terrorism offences, and more funding for counter-terrorism operations.

Amman, who was jailed for three years and four months in December 2018, had been staying in a hostel for newly-released prisoners in Streatham since his release.

As part of what police said was a "proactive counter-terrorism surveillance operation", plain-clothes armed officers were following him on foot.

Amman stole a knife from a shop, then attacked a woman, then a man further up the high road, before being gunned down.

Eyewitness video footage showed him writhing on the pavement outside a pharmacy as plain-clothes armed police officers pointed hand-held weapons at him and urged passers-by to get to safety.

Amman had a dark vest with silver canisters strapped to his body.

Amman's mother told Sky News television that her son was a "nice, polite boy".

Haleema Faraz Khan said he seemed "normal" when she visited him on Thursday, and he called her before yesterday's attack asking her to make him some mutton biryani.

Ms Khan, who is originally from Sri Lanka, said she thought the eldest of her five sons had become radicalised in prison.

"He was watching and listening to things online which brainwashed him," she said.

"Before he went to prison, he was not that religious. After he came out, he was really religious."

Police cordons remained in place at the scene in Streatham, as forensics officers gathered evidence.

Of the two people stabbed, a man in his 40s was being treated in hospital for his injuries, which were said to be non-life-threatening. A woman in her 50s was discharged.

A third victim, a woman in her 20s, was treated for minor injuries thought to have been caused by broken glass following the shooting.

Counter-terror officers were conducting searches at the hostel and a home in Bishop's Stortford, north of the capital near London Stansted Airport.

London Mayor Sadiq Khan said there were "roughly" more than 70 people in London who have been convicted of a terrorist offence, served time in prison and have been released.