Police are asking people to avoid Parliament Square, Whitehall, Westminster Bridge, Lambeth Bridge, Victoria Street up to the junction with Broadway and the Victoria Embankment up to Embankment Tube.
The Thames has been closed from Vauxhall to Embankment as part of the security response, after a member of the public, believed to have been hit by the car, was recovered from the water near Westminster Bridge.
The closure of the river, along with roads in the centre and Westminster, used by thousands of people visiting and working in Whitehall every day, caused temporary chaos in central London.
Dozens of people were stranded in the air at the top of the London Eye, which stopped amid the carnage in Westminster.
The huge security increase comes just days after Britain banned electronic devices such as laptops from the cabins of UK-bound planes from six Middle Eastern nations amid fears they could be used to blow up planes.
The death toll so far stands at five, including the attacker, who was shot after stabbing a police officer with a knife. The officer suffered fatal injuries and has also died, police have now confirmed.