A police officer was also stabbed in the nearby Houses of Parliament by an attacker, who was shot by police.
The attacker struck several pedestrians as he drove a car across the bridge, before crashing it into railings.
A number of other people were hurt – some with “catastrophic” injuries – a doctor at St Thomas’ Hospital said.
Lawmakers said they had heard three or four gunshots and staff inside Parliament were told to stay inside their offices.
A Downing Street source said PM Theresa May was safe.
Theresa May was seen being ushered into a silver Jaguar car as what sounded like gunfire rang out at Parliament during the incident.
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