Reports from social media show people lying in the road on Westminster Bridge and just outside Parliament.
The BBC said police believed there was a suspect vehicle outside parliament but police did not immediately confirm that report.
The incident occurred at around a quarter to three, London time (9:45 A.M. Eastern Standard Time). It appears that he deliberately drove into pedestrians and policemen who were using the bridge at the time.
Bradford Buck, from CT in the U.S., saw the incident unfolding and took cover with his wife.
Sky News reported two people had died, but the total number of casualties was unclear.
"I saw a fairly thick-set man wearing black clothes, running through the open gates", Letts said on MSNBC. Authorities said the attack was linked to a failed vehicle bombing a day before in London's West End, where an ambulance crew outside a nightclub spotted smoke coming from a Mercedes that turned out to be rigged with explosives.
Ambulance and fire service workers on Westminster Bridge after the attack.
Curious tourists and schoolchildren approached the police cordon, eager to see what was happening.
French Prime Minister Bernard Cazeneuve said French school pupils are among the injured and offered "solidarity with our British friends, and full support" for the wounded students and their families.US President Donald Trump spoke to May after the attack and pledged full cooperation and support of the US Government in responding to the attack.
For Sam and Osmond, both 17, this was one reason why the attack wasn't a surprise. But they did wonder why the attacker chose such a well-patrolled area of the capital.
"Lives have been lost and people have been seriously injured", he said. The police have obviously got to keep everybody safe and I commend them for what they are doing. "Here, it's a really stupid place to do it", Osmond said.
On Saturday, a man who had been investigated for links to radical Islam was shot dead at Paris's Orly airport after attacking a soldier on patrol and grabbing her rifle.
Not all of the injured were taken directly to the hospital.
"Whenever I have an emotion, whichever it is, I need to express it with my works". Then I got all these messages from my children asking if I was okay.
"Our sympathy goes out to the victims, in particular the policeman who died in the line of duty and those others who were slain".
'We will all move forward together, never giving in to terror and never allowing the voices of hate and evil to drive us apart'. Then it came across the bridge [and] crashed into a gate; the front end is smashed up. The anti-terrorist phone line, which concerned citizens are encouraged to use if they have any suspicions, received more than twenty-two thousand calls over the preceding year. Other MPs were kept in the House of Commons chamber until just before 8 p.m. - five and a half hours after the event - where they gave police a spontaneous round of applause. "There were maybe a dozen [injured]", she said.
But as the sun set on a day of horror, an eerie calm settled on the deserted streets outside.