British counter-terrorism police were investigating the background of an attacker who killed four people and injured about 40 before being shot to death by police just outside the British parliament in London.

Police have described the attack on Wednesday as a "marauding terrorist incident" and said they were working on the assumption that it was "Islamist-related". Police believe they know the identity of the attacker but have not named him.

Armed police raided a house in Birmingham overnight. The local police force, West Midlands Police, referred questions about the raid to London's Metropolitan Police, which is in charge of the investigation into the attack on parliament.

Police made several arrests during the raid, which was connected to the investigation, Sky News television channel reported on Thursday, citing unidentified sources. The Met Police declined to comment on whether there was a link.

Britain's most senior counter-terrorism officer, Mark Rowley, was due to make a statement at 0730 GMT.

The attack on Wednesday started when the assailant sped across Westminster Bridge in a car, ramming pedestrians along the way. He then ran towards parliament and stabbed a policeman before he was shot.

The dead were the assailant, the policeman he stabbed and three people who were hit by the car. Others were in hospital with very serious injuries.

Three French high-school students aged 15 or 16, who were on a school trip to London with fellow students from Brittany, were among the injured.

French Foreign Minister Jean-Marc Ayrault was expected to arrive in London to visit them at hospital, French media reported.

Westminster Bridge remained cordoned off with a strong police presence. The nearby Westminster underground train station, normally a busy hub in the morning rush hour, was not accessible from street level as it was within the cordon.

Parliament was due to convene later in what Prime Minister Theresa May said late on Wednesday was a sign that the attack would not disrupt British democracy or normal life in the capital.