Seven arrests have been made in raids following the Westminster attack that left four dead, police have said.
Acting Deputy Commissioner and Head of Counter Terrorism Mark Rowley said hundreds of detectives have worked through the night, carrying out searches at six addresses.
Those who died were a woman in her 40s, a man in his 50s, PC Keith Palmer and the attacker, he said.
Seven of the injured are still in hospital in a critical condition.
A further 29 had been treated in hospital, Mr Rowley added.
In the attack on Wednesday, a man drove a car along a pavement in Westminster knocking down pedestrians, leaving dozens injured.
He then stabbed a policeman and was shot dead by police in the grounds of Parliament.
In a statement made outside Scotland Yard, Mr Rowley said: “The inquiries in Birmingham, London and other parts of the country are continuing.
“It is still our belief – which continues to be borne out by our investigation – that this attacker acted alone and was inspired by international terrorism.
“To be explicit, at this stage we have no specific information about further threats to the public.”
He said he would not name the bridge victims yet, who were “a mix of nationalities”, and urged journalists not to publish the attacker’s name while searches were continuing.
He said Londoners should expect to see more police officers on the streets, after officers’ leave had been cancelled and duty hours extended.
It was initially thought that three members of the public had been killed on Westminster Bridge, but Mr Rowley referred to just two in his statement.
One of the raids by armed police, thought to be linked to the attack, took place in Hagley Road, Birmingham, on Wednesday night. A witness told the Press Association: “They came and arrested three men.”
BBC Newsnight reported there was a suggestion the car used in the attack was hired from an address in Birmingham, although this has not been confirmed.
Defence Secretary Sir Michael Fallon told BBC Radio 4’s Today programme the “working assumption” was that the attack was linked to “Islamic terrorism in some form”.
He paid tribute to Pc Palmer, a 48-year-old father and husband, and an unarmed member of the Parliamentary and Diplomatic Protection Squad who had served for 15 years.
Pc Palmer stopped the attacker getting into Parliament and “gave his life for the democracy we all cherish”, he told BBC Breakfast.
Parliament will sit, as normal, later, with the prime minister expected to make a statement.
Asked about the mood of the city, Sir Michael said: “London is getting back to normal. They’ve seen terrorism like this before and they are not going to let it triumph.”
Brendan Cox, the husband of murdered MP Jo Cox, said it was important to remember that “this was a story about people who didn’t come home yesterday”.
* The Cabinet Office says it will observe a one-minute silence at 9.33 am to pay respect to the victims
* The flag over the Houses of Parliament is flying at half mast
* Security at Parliament will be reviewed, says Sir Michael
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