Searches were being carried out in Staffordshire, where Khan had been living. He targetted the event, where dozens of people, including students and former prisoners, were present, the BBC said.
"While we are still in the early stages of the investigation, at this time we are not actively seeking anyone else in relation to the attack," Basu added.
"However, we continue to make fast time enquiries to ensure that no other people were involved in this attack and that there is no outstanding threat to the public."
The attack on the bridge across the Thames began at an event at Fishmonger's Hall at 1.58 p.m. Television images captured Khan brandishing a knife as he walked across the bridge. He was shot dead by officers after members of the public restrained him.
The Times reported that Khan's release from prison last year came after he agreed to wear an electronic tag and have his movements monitored.
The incident evoked memories of the 2017 terror attack on the same bridge when a van was deliberately driven ploughing the pedestrians before its three occupants ran to the nearby Borough Market area and began stabbing people in and around restaurants and pubs, leaving eight people dead and 48 injured.
The attackers, who claimed allegiance to the Islamic State, were shot dead by the police.