A man arrested on suspicion of attempted murder following a multiple stabbing had been released from custody shortly beforehand.
A 62-year-old woman was airlifted to hospital with life-threatening injuries after the attack in a Sainsbury's car park in Hampton, west London, on Friday morning.
Three other women, aged 53, 67 and 71 were also stabbed in the incident, but their injuries were not life threatening.
The 66-year-old suspect was arrested at the scene after police officers witnessed him holding a knife and chasing people.
It has since emerged that the man was arrested in another borough on Thursday on suspicion of being in possession of a knife and assaulting a police constable.
He was released from custody on Friday morning ahead of a court appearance next month.
A woman working at a nearby pub said the car park attack appeared to be unprovoked.
"He only went for the women," she said.
"The man ran through and started attacking them. It didn't seem like they knew him.
"If it had been 10 or 20 minutes earlier there would have been children there because it's right outside a primary school.
"He was caught very quickly just outside the car park. He appeared to be out of it, on drugs or crazy.
"The woman who was badly stabbed in the back made it up to the police station and raised the alarm.
"She is well-known locally and always goes shopping there all the time."
Officers do not believe the incident was terror-related.
Chief Superintendent Glenn Tunstall said: "I would like to praise members of the public who rushed to the aid of the injured women and provided them with first-aid.
"Their bravery and the outstanding courage of the officers who were first on the scene and confronted the armed man is worthy of praise.
"An incident like this will cause considerable concern to the local community, and I would like to reassure them that uniform officers will be patrolling the area and can speak to anyone who has concerns.
"Enquiries are ongoing, but we are not looking for anyone else in relation to the incident."