Seven suspects were taken into custody in Britain as police on Thursday put the death toll in the terror attack in the heart of London at four.

Seven of the people wounded in the Wednesday attack near Parliament were still in hospital and in critical condition, police said. Twenty-nine were discharged from hospitals.

Mark Rowley, Acting Deputy Commissioner and head of Counter-Terrorism unit, said the dead included a woman in her 40s, a man in his 50s, police officer Keith Palmer and the attacker.

Most media reports earlier said three members of the public were killed when the lone attacker, who has not been identified and who was later shot dead, ran over pedestrians over the iconic Westminster Bridge.

He then stabbed the unarmed Palmer on the grounds of Parliament.

Rowley said hundreds of detectives worked through the night and carried out searches at six addresses, the BBC reported. Inquiries were held in London, Birmingham and other parts of the country.

"It is still our belief ... that this attacker acted alone and was inspired by international terrorism ... Islamist terrorism," Rowley said.

At least 40 people were hit on the crowded bridge when the attacker drove a 4x4 along the pavement, knocking down pedestrians before crashing into a fence below Big Ben.

One woman fell into the Thames from the bridge but was said to be alive, media reports said.

The intruder, described by a witness as "middle-aged and Asian", broke into the grounds of Parliament where he fatally stabbed the police officer with two knives.  

The policeman died at the scene. The attacker, shot by other police officers, died after he was taken to hospital.

On Thursday, Indian President Pranab Mukherjee and Prime Minister Narendra Modi joined world leaders to denounce the London killings.

"Shocked to hear of (the) terrorist attack in London," Mukherjee tweeted. He said India stood by the United Kingdom and that "terrorism must be met through collective action by the international community".

Modi said: "Deeply saddened... Our thoughts and prayers are with the victims and their families. At this difficult moment India stands with the UK in the fight against terrorism."

British Prime Minister Theresa May said the attack was "sick and depraved".

"The location of this attack was no accident," she said. "The terrorists chose to strike at the heart of our Capital."

Flags were lowered to half mast over Downing Street.

The US, France and the European Union strongly condemned the attack.

President Donald Trump spoke with Theresa May and applauded the quick response of British authorities.

French President Francois Hollande expressed solidarity with Britain. "We have to understand that terrorism concerns all of us, and France, which has been struck many times, can know what the British people are suffering today."

European Council President Donald Tusk said: "My thoughts are with the victims of the Westminster attack. Europe stands firm with the UK against terror and ready to help."

Witness Jayne Wilkinson said: "We were taking photos of Big Ben and we saw all the people running towards us. Then there was an Asian guy in about his 40s carrying a knife about seven or eight inches long.

"And then there were three shots fired, and then we crossed the road and looked over. The man was on the floor with blood.

"He had a lightweight jacket on, dark trousers and a shirt. He was running through those gates, towards Parliament, and the police were chasing him."

The Thames has been closed from Vauxhall to Embankment as part of security measures but London bounced back to life on Thursday.