Hundreds of detectives worked through the night, carrying out searches at six addresses.
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.
In the attack last afternoon, a man drove a car along a pavement on Westminster Bridge knocking down pedestrians, creating panic and leaving dozens injured.