Eight fire engines and around 60 firefighters were called to a fire at a block of flats on Bromley Road in Catford.
Part of a bin room on the lower ground floor of an eight-storey block was damaged by the fire. Six adults and a child were led to safety by firefighters and were assessed at the scene by London Ambulance Service crews. A further 50 people left the building before the Brigade arrived.
Station Commander Shaun Coltress, who was at the scene, said: "The fire started in a bin room on the lower ground floor and produced a significant amount of smoke.
"There were some local road closures so we advised motorists to avoid the area where possible."
The Brigade was called at 1711 and the fire was under control by 1822. Fire crews from Beckenham, Lewisham, Bromley, Forest Hill and surrounding fire stations were at the scene.
The cause of the fire is under investigation by the Brigade and the Metropolitan Police Service.