An unnamed 36-year-old man was arrested at the scene and is in police custody, New York Times reports.
The attacker, who was caught on video by bystanders, first drove a car into a home and then got out and began attacking passersby in the Thurlow Gardens area, stabbing multiple victims.
Other footage showed the suspect being tased by police before being apprehended.
Authorities have not released a possible motive but have called the attack unprovoked and do not believe it was a terror incident.
"At this time we understand the suspect went on to attack other members of the public and two police officers," the Metropolitan Police stated, per ABC News. "Police in London have been called and other emergency services are in Hainault, east London, at a serious incident in which a man with a sword has been arrested."
"We do not believe there is any ongoing threat to the wider community. We are not looking for more suspects," they added.
"This must have been a terrifying incident for those concerned. I know the wider community will be feeling shock and alarm," said Deputy Assistant Commissioner Ade Adelekan. "People will want to know what has happened and will we provide more information as soon as we can."
The suspect was also reportedly injured in the incident when his vehicle crashed into the house.
“Given his injuries, we have been unable to interview him," Assistant Commissioner Louisa Rolfe of the Metropolitan Police said. "We are trying to understand exactly what happened and why. This is an incident which has clearly shocked everyone."