Protesters taking part in the Million Mask March have spread from Trafalgar Square towards Westminster as well as down the Mall towards Buckingham Palace.
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Between 4,000 and 8,000 fighters of the so-called Islamic State are still thought to be in the area.
Police are trying to find the driver of the car following the incident in Kingfisher Close, Brownhills.
An unnamed man died at the scene, while a woman was pronounced dead after being taken to St George's Hospital, Tooting, south-west London.