Two people have been stabbed and a terrorist has been shot dead by British police following what is believed to have been an Islamist-inspired terror attack in London.

Sudesh Amman was wearing a fake bomb vest when he attacked people on a busy street in the area of Streatham on Sunday afternoon.

Amman (20), who was from north London, had been released from prison just days earlier after serving time for spreading extremist material.

He had been sentenced in December 2018 to three years and four months in jail after a court heard that he had shared his extremist views with those close to him, even encouraging his girlfriend to murder her parents.

Amman was under police surveillance at the time of the attack.

In the early hours of Monday, police said they were searching properties but no arrests had been made.

Two people were stabbed - a man aged in his 40s and a woman in her 50s.

The man was taken to hospital in a life-threatening state, but his condition has since improved.

The woman was discharged from hospital on Sunday night.

A police forensics officer works outside a Boots pharmacy at the scene in Streatham High Road, south London after a man was shot dead by armed officers | Image: Kirsty O'Connor/PA Wire/PA Images

A woman in her 20s was treated for minor injuries believed to have been caused by glass following police gunshots.

Video shows two officers with guns drawn approaching the body outside a Boots, before another plain-clothes officer on a high-powered motorbike pulls up.

They back off as the man on the ground lifts his head slightly and more armed officers arrive.

A 19-year-old student - who wanted to remain anonymous - said: "I was crossing the road when I saw a man with a machete and silver canisters on his chest being chased by what I assume was an undercover police officer - as they were in civilian clothing.

"The man was then shot. I think I heard three gun shots but I can't quite remember."

Another witness, Karker Tahir, said: "It was horrible seeing it. The man was on the floor and it looked like he had something which police said may be a device."

British Prime Minister Boris Johnson said: "My thoughts are with the injured victims and their loved ones following today's horrific attack in Streatham.

"I want to pay tribute to the speed and bravery of the police who responded and confronted the attacker - preventing further injuries and violence - and all of the emergency services who came to the aid of others.

"An investigation is taking place at pace to establish the full facts of what happened, and the government will provide all necessary support to the police and security services as this work goes on."

He also promised to announce "further plans for fundamental changes to the system for dealing with those convicted of terrorism offences".