Authorities said 40 people have been wounded and Parliament was locked down. A search is underway to make certain no other attackers are in the area - though police believe there was only one attacker.
Rowley said the dead policeman was one of the armed officers who guards Parliament. The other victims were on Westminster Bridge.
"We are satisfied at this stage that it looks like there was only one attacker. But it would be foolish to be overconfident early on," Rowley said.
An attacker stabbed a police officer and was shot by police on the grounds outside Britain's Parliament, sending the compound into lockdown Wednesday. Around the same time, a vehicle mowed down pedestrians on nearby Westminster Bridge. Authorities said they were treating the attack as a "terrorist incident until we know otherwise."
"There were people across the bridge. There were some with minor injuries, some catastrophic. Some had injuries they could walk away from or who have life-changing injuries," Colleen Anderson of St. Thomas Hospital said.
British port officials say they pulled a woman from the Thames River following the incident on Westminster Bridge.
The Port of London Authority says a female member of the public was recovered from the river, injured but alive.
The authority says it has closed the river between Vauxhall Bridge and Embankment while a major security operation is under way after a suspected terror attack at the Houses of Parliament in London.
The threat level for international terrorism in the UK was listed at severe. Wednesday was the anniversary of suicide bombings in the Brussels airport and subway that killed 32 people.
The incident in London unfolded within sight of some of the city's most famous tourist sites, including the London Eye, a large Ferris wheel with pods that have views over the capital. It stopped rotating and footage showed the pods full as viewers watched police and medical crews on the bridge, which has Big Ben at its north end.
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Labour Party lawmaker Mary Creagh said it was her understanding that between five and seven people were mowed down on the bridge.
Rick Longley told the Press Association that he heard a bang and saw a car mow down pedestrians and come to a crashing stop. Images from the scene showed pedestrians sprawled on the ground, with blood streaming from a woman surrounded by a scattering of postcards.
"They were just laying there and then the whole crowd just surged around the corner by the gates just opposite Big Ben," he said. "A guy came past my right shoulder with a big knife and just started plunging it into the policeman. I have never seen anything like that. I just can't believe what I just saw."
Dennis Burns, who was just entering Parliament for a meeting, told the Press Association he heard a radio message saying an officer had been stabbed. Police and security rushed outside as he was going in.
"When I got inside I was wondering what the hell was going on and I saw dozens of panicked people running down the street," he said. "The first stream was around 30 people and the second stream was 70 people. It looked like they were running for their lives."
Daily Mail journalist Quentin Letts said he saw a man in black attack a police officer outside Parliament before being shot two or three times as he tried to storm into the House of Commons.
"He had something in his hand, it looked like a stick of some sort, and he was challenged by a couple of policemen in yellow jackets," Letts told the BBC. "And one of the yellow-jacketed policemen fell down and we could see the man in black moving his arm in a way that suggested he was stabbing or striking the yellow-jacketed policeman."
Lett said the other officer ran to get help and the man in black ran toward the entrance.
"As this attacker was running towards the entrance two plain-clothed guys with guns shouted at him what sounded like a warning, he ignored it and they shot two or three times and he fell," he said.
As lawmakers were voting inside Parliament, they reported hearing the sound of gunshots.
Prime Minister Theresa May was at Parliament when the incident began, but her office says she is safe.
Authorities are bracing for possible violence during several marches Saturday, drawing thousands of both pro-and anti-EU participants.
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