Two people have died in the Westminster attack, Sky sources say, while several of those hurt have “catastrophic” injuries.
One of the victims has been confirmed as a woman, while the sex of the other is not known.
Three French schoolchildren are among the injured, France’s PM has said.
A woman has also been pulled alive from the Thames with serious injuries.
Westminster is on lockdown after the incident, which is being treated as a terror attack, in which a man ploughed a car into pedestrians before stabbing a police officer outside the Houses of Parliament.
The assailant has been shot.
Commander BJ Harrington of the Metropolitan Police said there were “a number of casualties”, including police officers, but could not comment on the numbers or nature of the injuries.
Eyewitnesses have said the attacker mowed down pedestrians on Westminster Bridge before crashing his car into railings outside the Houses of Parliament then running out with a knife, stabbing a police officer and then being shot.
Photos show several people injured on Westminster Bridge, some bleeding heavily, others lying in blood.
Ambulances rushed to the scene as the area was cordoned off.
Reporters with the Reuters news agency inside Westminster heard loud bangs.