The deadly attack near the Houses of Parliament yesterday afternoon saw the lone attacker shot dead by police after he used a car to run down pedestrians, killing two, and stabbing police officer to death.Leaders of France and Germany, which suffered deadly vehicle attacks last year, offered the UK their support.
The US president offered condolences and praised UK security forces.
Among the 20 people injured by the car on Westminster Bridge are three French schoolchildren and two Romanians.
In Paris, the lights of the Eiffel Tower went out from midnight (23:00 Irish Time / GMT) in a tribute to the victims.
The three French schoolchildren were among those injured when the terrorist's vehicle hit people on London's Westminster Bridge.
The French foreign ministry said they had been on a school trip to London.Le Telegramme
newspaper said they were teenagers from a private high school in Concarneau, north-western France.
Two Romanians, said to be a couple, were injured, and reports say five South Koreans were also hurt.
At least two of the French pupils are said to be in a critical condition.
Witnesses quoted by Le Telegramme said one pupil had ended up on the car bonnet.
The families of the three injured students are being flown by a military plane from the town of Lorient to be with them, the mayor of Concarneau, Andre Fidelin, said.
Parents have also gathered at the school, the Lycee Saint-Joseph.
The Romanians, named as Andrei and Andrea by English friend Patrick Tracey, were caught up in the attack as they were on their way to the London Eye, Mr Tracey said.
Romania's foreign ministry said they had been taken to a hospital for treatment, without giving further details, the Associated Press reports.
news agency reported that five South Korean tourists were injured, one seriously, in the attack.
It quoted a tour agency official as saying that they were now being treated at two hospitals.Arrests
Meanwhile Seven people have been arrested in raids in London, Birmingham and elsewhere linked to yesterday's Westminster terror attack.
Mark Rowley, the Metropolitan Police's senior anti-terror officer, said six addresses were raided overnight.
Mr Rowley said the death toll from the attack was four, not five.
The dead were: the attacker, police constable Keith Palmer, who he stabbed, and a woman in her mid 40s and a man in his mid 50s, who were mown down as the terrorist sped across Westminster Bridge in his car.
Mr Rowley said 29 people had been treated in hospital with seven people in a critical condition.
Mr Rowley said it was still his belief the attacker worked alone and was inspired by "international terrorism", adding that there was no specific information to suggest any further threat to the public.
A man who witnessed a raid on an address in Birmingham overnight told the Press Association
: "The man from London lived here."
Officers stormed a second-floor flat above a row of shops on Hagley Road at around 11pm, the witness said.
He added: "They came and arrested three men."
One of the flat's windows was covered in cardboard, with non-uniformed officers spotted taking pieces of equipment into the property.
As he was describing the events, the witness was interrupted by a police officer, who had been guarding the scene.
He had his details taken and was convinced to go to a police station with another officer.
Both the House of Commons and the House of Lords will sit at their normal times today, in a show of defiance in the wake of the attack.Two knives
Police officer Keith Palmer, a member of the Parliamentary and Diplomatic Protection Squad, was killed as he tried to stop the attacker at around 2.30pm, while two members of the public were also fatally injured.
The suspect, who was armed with two knives, injured around 30 others as he mowed down pedestrians with a car on Westminster Bridge before crashing at the gates in front of Parliament and stabbing the policeman before being shot dead by armed officers.
Prime Minister Theresa May praised the bravery of police officers last night as it was announced Westminster would attempt to run as smoothly as normal.
In a statement from Downing Street, she said: "Any attempt to defeat those values through violence and terror is doomed to failure.
"Parliament will meet as normal. We will come together as normal. And Londoners - and others from around the world who have come here to visit this great city - will get up and go about their day as normal.
"And we will all move forward together, never giving in to terror and never allowing the voices of hate and evil to drive us apart."