The four injured men were taken to hospital after the incident on Elmington Estate, Camberwell Road.
“[You] can’t see much from the road as the scene was deeper inside the estate,” witness Chris Hardley told Sky News.
“There were armed police circling the area in unmarked BMW X5s and an air ambulance took off nearby/”
He added: “There is certainly a problem with stabbings in the area and it was only last month that a guy got stabbed to death round the corner.”
Scotland Yard said officers were called to Landor House, Camberwell, shortly before 5.25pm.
Police are awaiting an update on the conditions of the victims, while a crime scene remains in place.
A London Ambulance Service spokesperson said: “We sent a number of resources to the scene including ambulance crews, a single responder in a car and an incident response officer.
“We treated four people at the scene and took them to hospital.”