People from 12 different countries, including three French teenagers, are among those injured in the Westminster attack.
Police said some of the people had "catastrophic injuries" and seven remain in a critical condition in hospital after the attack carried out by 52-year-old Khalid Masood.
Theresa May has visited victims being treated at one of the London hospitals, spending around 40 minutes meeting the injured and hospital staff.
Among the hurt are three police officers, two of whom are in a serious condition, who were hit on the bridge on their way back from a commendation ceremony.
Another person injured on the bridge was 19-year-old Travis Frain, who was hit by the attacker's car.
Seconds later he called his mother to say: "Mum I'm safe ... I know you'll be worrying."
The politics student, who had been in Parliament to watch Prime Minister's Questions, suffered a fractured leg and arm as well as other injuries.
His mother, Angela Frain, 46, said it "happened so fast I don't think he knew what had happened."
"I think it hit him on his side and he went over the bonnet," she said.
As well as 12 Britons the injured include three French students, two Romanians, four South Koreans, one German, one Polish national, one Irish citizen, one Chinese national, one Italian, one American and two Greeks.
The mother of one of the French students said she initially thought her son was dead.
"After an hour, we were told he was injured. It felt extremely long," she told French media.
She said he suffered a head injury and fractures to his legs when Masood drove down the pavement on Westminster Bridge.
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Her son had little memory of the attack, she said, but was "relieved and happy to see us" when his parents arrived in London on Wednesday evening.
The students, who are aged between 15 and 16, are pupils at the Lycee Saint-Joseph de Concarneau in Brittany.
The French Foreign Minister Jean-Marc Ayrault, who travelled to London to meet the students, said their conditions were not life-threatening and they would return home as soon as possible.
The American woman injured has been named by her family as Melissa Cochran and is the wife of victim Kurt Cochran .
The couple had been travelling in Europe to celebrate their 25th wedding anniversary, and were on the last day of their trip.
The woman who plunged into the Thames has been identified as a Romanian tourist, who was visiting London with her boyfriend to celebrate his birthday.
She was rescued from the water by a London Fire Brigade boat and given urgent treatment on a nearby pier.
She sustained serious head injuries and badly damaged lungs, and has since undergone surgery to remove a blood clot from her brain.
It is not yet clear if she jumped from the bridge or was thrown into the water by the speeding vehicle. She remains in a critical state.