House of Commons leader David Lidington said the "alleged assailant was shot by armed police".
The Met Police have since confirmed four people have died in the incident and at least 20 people have been injured.
Bomb squad officers are still on the scene dealing with a "suspect package" attached to a vehicle.
A number of others had been hurt, including people with "catastrophic injuries".
The French Prime Minister said that teenagers from France on a school visit to London were among those hurt.
Five people are believed to have been run down by a car and one of the fatalities was a woman pedestrian who was "under the wheel of a bus".
This is the full statement from Scotland Yard
/WalesOnline/
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