A counter-terrorism investigation is already under way into the attack at Westminster, police said.
A woman died on Westminster bridge and an officer was stabbed before an attacker was shot by police.
At least 10 patients have been treated on Westminster Bridge and a number of hospitals are on alert, London Ambulance Service said.
A spokesman for the Port of London Authority, which looks after safety on the River Thames, said: “A female member of the public was recovered from the water near Westminster Bridge. She is alive but undergoing urgent medical treatment on a nearby pier. We believe she fell from the bridge.”
He said the river has been closed from Vauxhall to Embankment “as part of the security response”.
Giving a statement outside Scotland Yard, police spokesman Commander BJ Harrington said: “A senior national coordinator has declared this a terrorist incident.
“Although we remain open-minded to the motive, a counter-terrorism investigation is already under way led by the Met counter-terrorism command.
“We received a number of different reports which included a body in the river, a car in collision with pedestrians and a man armed with a knife.
“Officers were already in the location as part of routine policing but immediately additional officers were sent.”
He said: “I would like to repeat our request for the public to avoid the following areas, Parliament Square, Whitehall, Westminster Bridge, Lambeth Bridge, Victoria Street up to the junction with Broadway and Victoria Embankment up to Embankment Tube station.
“This is to allow emergency services to deal with this ongoing incident.
“There is an ongoing investigation being led by the counter-terrorism command.
“We would ask anybody who has images or film of the incident to pass those to the police.
“We know there are a number casualties including police officers but at this stage we can not confirm numbers or the nature of these injuries.”
Prime Minister Theresa May is to chair a meeting of the Government’s emergency Cobra committee to discuss the immediate response to the incident.
The Cobra committee brings together government ministers with senior officials of the emergency services and security and intelligence agencies.
Meeting in a briefing room of the Cabinet Office on Whitehall, Cobra co-ordinates the high-level response to serious incidents, and has previously gathered after terrorist atrocities including the July 7 attacks on the London transport network and the murder of soldier Lee Rigby.
There was no immediate information on who will attend Wednesday’s meeting.
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