A 19-year-old was taken to hospital after staggering into a convenience store in Campshill Road, Hither Green, covered in blood at 5.55pm last night.
Officers were also called to Lewisham Park, where they found a 23-year-old with knife wounds.
A short time later, a 20-year-old man attended a south London hospital also with stab injuries.
Three men were arrested in a car parked outside on suspicion of possessing a weapon.
Police believe all three stabbings are connected, stemming from a pre-arranged fight in a car park in nearby Harvard Road.
Resident Rosie Tucker, 66, said: “There was screaming and shouting then all hell broke loose.
"It’s a real shock. It’s a lovely neighbourhood near the park.”
Meanwhile, a double stabbing left two men in their twenties injured opposite Kingsbury Tube station in Brent shortly after 10am.
None of the victims’ injuries are life-threatening and no arrests have been made.
