Ten fire engines and around 40 firefighters were called to a block of flats at Lewisham Road yesterday (July 8) at 11.55pm after 14 calls were made.
One woman was treated at the scene by medics and three other people left the building before the London Fire Brigade arrived.
A flat split between a ground and first floor was destroyed in the fire.
Part of another flat between the second and third floor was damaged by the fire.
Lewisham Road was closed between Penrose Way and Lewisham Hill.
The fire was eventually under control by 2.02am today (July 9).
The cause of the fire is unknown at this time, but the brigade continues to investigate.