Six fire engines and around 40 firefighters were called to a fire at a block of flats on Becton Place in Erith.
A ground floor pram shed was destroyed by the blaze. One man was treated at the scene for smoke inhalation by London Ambulance Service crews.
The Brigade was called at 2114 and the fire was under control by 2210. Fire crews from Bexley, Erith, Lee Green, Sidcup, Eltham and East Greenwich fire stations were at the scene.
The cause of the fire is under investigation by the Brigade and the Metropolitan Police Service.