A man wearing a "hoax device" has been shot dead after stabbing two people in a terrorist attack on a high street in London's south, police say.

Key points: A witness saw a man "with a machete and silver canisters on his chest"

A witness saw a man "with a machete and silver canisters on his chest" Two people have been injured, at least one of them seriously

Two people have been injured, at least one of them seriously In a similar incident in November, police shot dead a man wearing a fake suicide vest who stabbed several people near London Bridge

The two victims were injured, at least one of them seriously, according to local member of Parliament Bell Ribeiro-Addy.

Police said the attack on a street in Streatham was believed to be Islamist-related and that officers had found a hoax device strapped to the man they shot dead.

"Cordons were put in place and it was quickly established that this was a hoax device," said Lucy D'Orsi, Deputy Assistant Commissioner in the Metropolitan Police.

"The incident was quickly declared as a terrorist incident and we believe it to be Islamist-related."

British media have reported the suspect as Sudesh Amman who was released from prison about a week ago after serving half of his three-year sentence for terror offences.

Gulled Bulhan, a 19-year-old student from Streatham, told Britain's Press Association he witnessed the attack.

"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," he said.

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

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Mr Bulhan said he ran into a local library to seek safety.

"From the library I saw a load of ambulances and armed police officers arrive on the scene," he said.

Karker Tahir, a man who was working nearby, told Sky News the suspect was shot three times. Police told people in the area to leave because the man had a bomb in his bag, Mr Tahir said.

Several unverified videos of the scene have been posted on Twitter. In one, a man can be seen lying on the ground of a street as at least two police officers behind an unmarked car point their guns.

Another video shows helicopters overhead and police cars in the surrounding streets.

Police officers control a street in south London following a stabbing. ( Reuters: Simon Dawson )

Former deputy assistant police commissioner Stephen Roberts said police would quickly try to search the suspect's residence and seize any computer devices to scour his internet records.

Investigators would research the man's background to learn more about the attack and any possible co-conspirators, Mr Roberts said.

He said if the facts showed the stabbings were carried out by a "self-starter", it meant any city in the country was vulnerable at any time to a similar sort of low-tech attack.

Police said the incident happened in a bustling residential area that did not boast any major British landmarks like areas hit by earlier attacks.

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Incident 'looks very similar' to London Bridge attack

The last similar terrorist incident in London was in November, when police shot dead a man wearing a fake suicide vest. He stabbed two people to death and injured three more before being wrestled to the ground by bystanders.

Chris Phillips, the former head of the National Counter Terrorism Security Office, told the BBC the incident "looks very similar to what we saw on London Bridge just a few months ago".

"We can only hope that police have dealt with it fully now and that it's one person acting alone," he said.

London Mayor Sadiq Khan released a statement praising emergency workers.

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"A man has been shot dead by armed police in Streatham following an incident that is being treated as terrorism-related. A number of people are believed to have been stabbed," Mr Khan said.

"I am in close contact with the Met Commissioner and local representatives, and want to thank our police, security and emergency services staff for their swift and courageous response."

British Prime Minister Boris Johnson also thanked emergency services staff.

"Thank you to all emergency services responding to the incident in Streatham, which the police have now declared as terrorism related," Mr Johnson said.

"My thoughts are with the injured and all those affected."

The BBC said witnesses reported hearing two gunshots just after 2:00pm on Sunday (local time).

A man was shot dead by police officers in Streatham, south London. ( Reuters: Antonio Bronic )

According to the BBC, early reports indicate a man went into a shop with a knife and started stabbing people.

The reports said the man came out of the shop and stabbed a woman — possibly on a bicycle.

At that point it seems the alarm was raised and the police arrived, firing three shots and killing the alleged terrorist.

Meanwhile, London's Metropolitan police urged people not to listen to rumours or unsubstantiated reports on social media about the incident.

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They said they would release facts when they had them.

They earlier also asked people to "use common sense and restraint" in circulating pictures and videos of the Streatham incident, including images of the officers involved.

British authorities on November 4 reduced the national threat level to "substantial", meaning an attack is considered likely.

That is the third-highest level in a five-step alert system used by British authorities and marks the first time the threat level has been so low since August 2014.

Reuters/AP