Westminster attacker Khalid Masood acted alone and there was no evidence to suggest that any more attacks were planned, the Metropolitan police said.
Deputy Assistant Commissioner Neil Basu said in a statement: "We still believe that Masood acted alone on the day. We must all accept there is a possibility we will never understand why he did this. That understanding may have died with him."
"Nevertheless we are determined to understand if Masood was a lone actor inspired by terrorist propaganda or if others have encouraged, supported or directed him," Basu added.
The 52-year-old attacker was shot dead after killing four people when he drove his car into pedestrians before stabbing a police officer. At least 50 people were injured in the attack.
Islamic State (Isis) claimed responsibility for the attack and police have since focused on whether Masood had accomplices. After the attack, police also raided many properties in England and arrested at least 11 people but only one remained in custody on Saturday (25 March), according to Reuters.
The attacker, who used many aliases, had previous criminal convictions but none for terrorism. He was registered as Adrian Elms at birth and took his stepfather's name and became Adrian Ajao later on as child.