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Britain on Monday promised an urgent overhaul of 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 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.

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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, on Sunday.

The Islamic State's 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, 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.