When officers arrived they found three women at the location with knife wounds while a fourth woman was found nearby with life-threatening injuries.
A Metropolitan Police spokesman said a man in his 60s was arrested at the scene on suspicion of attempted murder.
A Taser was deployed during the suspect’s arrest but it was not discharged.
The spokesman said: “Officers attended and discovered three women suffering from knife wounds.
“The London Ambulance Service also attended and are providing treatment to the women. Their conditions are not thought to be life-threatening or changing at this time.
“A fourth woman who had also suffered knife wounds was subsequently located at a nearby property. She has been taken to hospital where her condition at this stage is thought to be life-threatening.”
A woman working at a nearby pub said the 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 it was completely unprovoked.
“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.”
A member of staff at Tangley Park Children’s Centre, which backs onto the scene, said: “We kept all the children safe and kept them in the building until we knew it was safe.
“It’s just such a shock – our parents and children could have been walking to their cars at that time.
“Our sympathies go out to everyone who was hurt and we are really glad none of our families were involved.”
The incident is not thought to be terror related.