Mark Rowley said among the injured were Australian, British and Israeli citizens. None have life threatening conditions.
He said the attacker was a Norwegian man of Somali origin.
Police investigating the attacks are close to ruling out a terror motive, saying “mental health” was a significant factor.
“The investigation is fast paced and we are making urgent progress.
“While the investigation is not yet complete, all of the work that we have done so far increasingly points to having been triggered by mental health issues.
“At this time we believe this was a spontaneous attack and that the victims were selected at random.”
The 19-year-old suspect has been arrested on suspicion of murder and is being detained in a South London police station.
Police say they have interviewed the suspect’s family and searched his address. They have also liaised with MI5 and MI6, and neither was aware of him.
Rowley said police had “searched addresses in north London” and