Seven arrests have been made in raids in London, Birmingham and elsewhere following an attack in Westminster that left four dead, police have said.
Hundreds of detectives have worked through the night, carrying out searches at six addresses, Acting Deputy Commissioner Mark Rowley said.
The dead are PC Keith Palmer, Aysha Frade who worked at a London college, a man in his 50s and the attacker.
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 on Westminster Bridge knocking down pedestrians, creating panic and leaving dozens injured.
He then ran towards Parliament where he stabbed PC Palmer who was unarmed. Armed police then shot dead the attacker in the grounds.
Mrs Frade worked at a London sixth form college just a few hundred metres from Westminster Bridge.
Principal at DLD College, Rachel Borland, said she was “highly regarded and loved by our students and by her colleagues”.
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.