Five people were killed, including the assailant, and 40 others were injured in what Prime Minister Theresa May condemned as a "sick and depraved terrorist attack."
Lawmakers, lords, staff and visitors were locked down after the man was shot by police within the perimeter of Parliament, just yards (meters) from entrances to the building itself and in the shadow of the iconic Big Ben clock tower. He died, as did three pedestrians on the bridge, and the police officer.
A doctor who treated the wounded from the bridge said some had "catastrophic" injuries. Three police officers, several French teenagers on a school trip, two Romanian tourists and five South Korean visitors were among the injured.
British Prime Minister Theresa May condemned the "sick and depraved terrorist attack" in London.
Earlier it was reported that a woman had died and other people were being treated for "catastrophic" injuries after a car crashed into pedestrians near the British parliament and an assailant stabbed a policeman in what police called a terrorist incident.
The knifeman was then shot by police when he had tried to force his way into a courtyard just outside the Houses of Parliament.
"We've declared this as a terrorist incident and the counter-terrorism command are carrying out a full-scale investigation into the events today," Mark Rowley, Britain's most senior counter-terrorism officer, told reporters.
May has ordered flags to be lowered to half-mast over Downing Street as a mark of respect to the innocent people who lost their lives in the attack outside parliament on Wednesday, the BBC reported.
The announcement comes as she chairs a meeting of the government's emergency Cobra committee, which deals with major emergencies. The Cobra committee brings government ministers together with senior officials of the emergency services and security and intelligence agencies.
The incident appeared to have unfolded in several locations, including on nearby Westminster Bridge where eyewitnesses said a car had crashed into pedestrians.
Reuters reporters inside parliament heard loud bangs and shortly afterwards saw two people lying on the ground in a courtyard just outside.
A Reuters photographer said he saw at least a dozen people injured on the bridge. His photographs showed people lying on the ground, some of them bleeding heavily and one under a bus.
Sky News reported two people had died, but the total number of casualties was unclear. The London Ambulance Service said it had treated at least 10 people on the bridge.
The incident took place on the first anniversary of attacks by Islamist militants that killed 32 people in Brussels.
"Officers - including firearms officers - remain on the scene and we are treating this as a terrorist incident until we know otherwise," police said in a statement.
"We know there are a number of casualties including police officers but at this stage we cannot confirm numbers or the nature of these injuries," Commander BJ Harrington told reporters.
"We received a number of different reports which included a person in the river, a car in collision with pedestrians and a man armed with a knife."
A woman was pulled alive, but with serious injuries, from the Thames, the Port of London Authority said.
French Prime Minister Bernard Cazeneuve said three French nationals were injured. French media reported they were high-school students.
Messages of support
May's office in Downing Street issued a statement saying her thoughts were with those killed and injured in the terror attack on Wednesday, according to AFP.
Other world leaders, meanwhile, offered their own messages of support.
German Chancellor Angela Merkel expressed shock at the attack, saying her thoughts were with the British people and everyone in the capital, according to Reuters.
French President Francois Hollande expressed support and solidarity with Britain.
US President Donald Trump offered his condolences to the British prime minister, offering full cooperation and support from the US.
Car "out of control"
"I just saw a car go out of control and just go into pedestrians on the bridge," eyewitness Bernadette Kerrigan told Sky News. She was on a tour bus on the bridge at the time.
"As we were going across the bridge, we saw people lying on the floor, they were obviously injured. I saw about 10 people maybe. And then the emergency services started to arrive. Everyone was just running everywhere."
Officials said an assailant had stabbed a policeman and then been shot.
Witness reports suggested the assailant and the stabbed policeman were the people seen lying on the ground outside the parliamentary building.
The House of Commons, which was in session at the time, was immediately suspended and lawmakers were asked to stay inside.
Prime Minister Theresa May was safe after the incident, a spokesman for her office said. He declined to say where May was when the attack took place.
Journalist Quentin Letts of the Daily Mail newspaper told LBC radio that he had witnessed the stabbing of the policeman and the shooting of the assailant from his office in the parliament building.
"He (the assailant) ran in through the open gates ... He set about one of the policemen with what looked like a stick," Letts said.
"The policeman fell over on the ground and it was quite horrible to watch and then having done that, he disengaged and ran towards the House of Commons entrance used by MPs (members of parliament) and got about 20 yards or so when two plain-clothed guys with guns shot him."
Reuters reporters inside parliament saw a large number of armed police, some carrying shields, pouring into the building. A helicopter ambulance landed on Parliament Square.
U.S. President Donald Trump told reporters at the White House he had been briefed on events in London but gave no details.
In Edinburgh, the Scottish parliament suspended a planned debate and vote on independence as news of events in London came in.
Britain is on its second-highest alert level of "severe" meaning an attack by militants is considered highly likely.
In July 2005, four British Islamists killed 52 commuters and themselves in suicide bombings on the British capital's transport system in what was London's worst peacetime attack.
*The story was edited by Ahram Online.