The London Ambulance Service also confirmed: "We have a number of resources attending an incident in Streatham High Road".
The police force said the incident occurred in the London's Streatham neighborhood.
Police said the man they had shot had been pronounced dead.
Gunshots were heard just after 2pm Sunday.
Prime Minister Boris Johnson said he will announce plans on Monday for "fundamental changes to the system for dealing with those convicted of terrorism offences" following the attack.
BBC journalist Steffan Powell, in Streatham, said armed police were everywhere and had been telling residents to stay inside. Witnesses reported seeing the man wearing what looked like a suicide vest. he was wearing a suicide vest.
Police said the scene of the incident was now fully contained.
"After that I ran into the library to get to safety".
Visuals from the street showed several emergency services vehicles on the roads, according to The Guardian.
A man is surrounded by police after an incident on London Bridge in London on Nov. 29 2019
A witness to the attack described seeing a man "with a machete and silver canisters on his chest" fleeing from plain-clothes police before they opened fire.
Social media showed multiple ambulances on the scene and helicopters in the air as helicopters responded to the incident.
"A man has been shot by armed officers in #Streatham". "But he didn't stop, and then I saw that they shot him three times".
The Metropolitan Police said it was awaiting updates on the condition of those injured.
Stephen Roberts, a former deputy commissioner for the Metropolitan Police, said authorities would quickly try to search the suspect's home and seize any computer devices to scour his internet records.
The Metropolitan Police said in a tweet that it believed two persons have been stabbed and that the incident had been declared terror-related.
Mayor of London Sadiq Khan thanked emergency services for their "swift and courageous response", saying: "They truly are the best of us".
Britain downgraded the country's terrorism threat level from "severe" to "substantial" - warning a terrorist attack is "likely" rather than "highly likely - in early November, its lowest rating in more than five years".
Trump asked Bolton to join pressure campaign in Ukraine in early May
The Senate is conducting an impeachment trial over allegations that Trump abused his office and obstructed Congress. Trump, a Republican, will make lowering the cost of healthcare a key part of his speech, the official said.