Several videos of the scene were posted on Twitter, but not verified by Reuters. In one, filmed from inside a shop across the road, a man can be seen lying on the street while at least two armed police officers point their guns from behind an unmarked car with its blue lights flashing.
At least one helicopter flew overhead and police cars were in surrounding streets, with the area blocked off by tape.
Prime Minister Boris Johnson said on Twitter: "Thank you to all emergency services responding to the incident in Streatham, which the police have now declared as terrorism-related".
"My thoughts are with the injured and all those affected," he added.
The last such incident in London was in November, when police shot dead a man wearing a fake suicide vest who stabbed two people to death and wounded three more before being wrestled to the ground by bystanders.
That attack was carried out by a man with Islamist militant sympathies. He had been jailed for terrorism and released early.
London's mayor, Sadiq Khan, said in a statement after Sunday's incident: "Terrorists seek to divide us and to destroy our way of life - here in London we will never let them succeed."
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