London police say five people, including the attacker, were killed after a car ploughed into pedestrians and a man went on a stabbing spree before being shot dead close to the British parliament.

Around 40 others were wounded in Wednesday's attack that caused chaos in one of the city's busiest locations.

Deputy London Metropolitan Police Commissioner Mark Rowley said investigators suspect the attacker had been "inspired by international terrorism".

"Islamist-related terrorism is our assumption," Rowley told reporters.

REPORTER'S NOTEBOOK: Seeking solace in wake of Westminster attack

He said police believed they knew the identity of the attacker but he declined to provide details.

Rowley said the violence started when a car was driven over Westminster Bridge, hitting and wounding a number of civilians and three police officers.

The car then crashed into railings just outside parliament where a man armed with a knife continued the attack and tried to enter the building.

The assailant was shot dead after he stabbed to death a policeman. The other three victims were among those hit by the car.

Many people were lying on the ground - some bleeding heavily and apparently unconscious - after the attack, which Prime Minister Theresa May condemned as "sick and depraved".

"The location of this attack was no accident," she said in a statement outside her Downing Street office late in the evening.

"The terrorist chose to strike at the heart of our capital city, where people of all nationalities, religions and cultures come together to celebrate the values of liberty, democracy and freedom of speech."

Some of the wounds suffered by the victims were described as "catastrophic". One woman was pulled out alive by port authorities from the River Thames with serious injuries.

Witnesses initially reported a number of attacks near parliament.

"We saw a black vehicle at full speed and it ran down a number of people. I could see people flying all around," tourist Babi Nagy told Al Jazeera. "Immediately it came to mind this was a terrorist attack."

Polish politician and journalist Radoslaw Sikorski posted a video on Twitter of the aftermath on the bridge, showing several wounded people lying on the ground.

A car on Westminster Bridge has just mowed down at least 5 people.pic.twitter.com/tdCR9I0NgJ — Radosław Sikorski (@sikorskiradek) March 22, 2017

Another witness said he saw victims scattered along the street.

"As I was walking up the steps, there was a man who had fallen and medics were taking care of him. There was a lady who was also stabbed or shot. There was a lot of blood," Martin Pearce told Al Jazeera at the scene.

The last major attack to hit London was in July 2005, when a coordinated series of bomb blasts targeted its public transportation system during rush hour. The bombings killed 52 people and wounded more than 700 others.

Mayor Sadiq Khan said Londoners will "never be cowed by terrorism".

"There will be additional armed and unarmed police officers on our streets from tonight in order to keep Londoners, and all those visiting our city, safe," he said.

"I want to reassure all Londoners, and all our visitors, not to be alarmed."

International messages of condolence were offered to the United Kingdom.

Chancellor Angela Merkel said Germany stood by Britain following the deadly attack.

"Although the background to these acts are not yet clear, I reaffirm that Germany and its citizens stand firmly and resolutely alongside Britons in the struggle against all forms of terrorism," Merkel said in a statement.

US President Donald Trump offered May the full cooperation and support of the United States in responding to the attack, the White House said in a statement.

Turkish President Recep Tayyip Erdogan sent a letter of condolences to the British prime minister.

"I want to emphasise that Turkey deeply feels and shares the United Kingdom's sorrow. Turkey always stands in solidarity with the friendly and allied United Kingdom in the fight against terrorism, one of the greatest threats to international peace and security," he said.

In Paris, the lights of the Eiffel Tower were switched off. Three French schoolchildren on a visit to London were injured in the attack.