The man shot dead by police after strapping a fake bomb to his chest and embarking on a stabbing rampage in a busy London street had recently been released from jail after serving time for terrorism-related offences.

Deputy Assistant Commissioner Lucy D’Orsi said police identified the attacker as 20-year-old Sudesh Amman. He had been convicted for publishing graphic terrorist videos online and had stockpiled instructions on bomb-making and knife attacks, according to police.

Officers had been trailing Amman at the time of Sunday’s attack, Ms D’Orsi said, but were unable to head off the bloodshed in the commercial and residential south London neighbourhood of Streatham.

The incident in London recalled a November stabbing attack carried out by another man who had served prison time for a terrorism offence. Two people were killed in that attack.

Metropolitan Police released this photo of Sudesh Amman. Photo: AAP

British Prime Minister Boris Johnson said measures would be introduced on Monday to bring “fundamental” change to the way people convicted of terrorism offences are handled in prison and afterward.

“The suspect had been recently released from prison where he had been serving a sentence for Islamist-related terrorism offences,” Ms D’Orsi said of Sunday’s attacker.

It seems likely the victims will survive. A man in his 40s thought to be in life-threatening condition has improved, and a woman who had been hospitalised has been released.

Another female victim is still in the hospital with lesser injuries, possibly caused by flying glass after the attacker was shot dead.

Ms D’Orsi said the incident started at 2pm.

“Armed officers, who were part of a proactive counterterrorism operation and were following the suspect on foot, were in immediate attendance and shot a male suspect dead at the scene,” she said.

She said police saw a device strapped to the attacker’s body and called in specialist officers who quickly determined the purported explosive device was a hoax.

• Read the full police statement here

Officials praised the police action but questions are likely to be raised about why the officers trailing Amman could not prevent the attack.

Amman reportedly entered a shop carrying a large knife in the Streatham neighbourhood and started randomly stabbing people.

It’s believed he left the shop and then attacked a female cyclist

Video from the scene appeared to show three undercover police officers in an unmarked car making a quick stop just after the attack.

Streatham resident Nardos Mulugeta recalled hearing gunshots then seeing victims lying hurt on the ground.

“I went over and I saw the first victim, a male victim on the ground, near the White Lion Pub, and people were helping him,” the 52-year-old said.

“Then five minutes later a woman came over and said ‘I’ve been stabbed, too, in the back’. And then people starting helping her.

“I saw one body laying down further away. He was face-down between Argos and Iceland. It’s really scary.”

Ms D’Orsi said there was no “continuing danger” to the public, but the area remained cordoned off as the investigation continued.

The drama, about eight kilometres south of central London, marked a departure from recent terror attacks in the British capital that took place near landmarks such as London Bridge and the Houses of Parliament.

The attack caused chaos and panic on what had been a typical Sunday afternoon, with the streets filled with shoppers.

In November, British authorities lowered the national terror threat level to “substantial,” meaning an attack is considered likely.

London Mayor Sadiq Khan urged community resolve in the face of another attack.

“Terrorists seek to divide us and to destroy our way of life,” he said.

“Here in London we will never let them succeed.”

-with AAP