Four fire engines and around 25 firefighters were called to a fire at a block of flats on Rotherhithe Road in Deptford.
The balcony of a flat on the first floor of a 16-storey block was destroyed by the fire and a small part of the flat was damaged. Around 50 people left the building before the Brigade arrived. No injuries were reported.
The Brigade was called at 0757 and the fire was under control by 0845. Fire crews from Deptford, Old Kent Road, Dockhead and Peckham fire stations were at the scene.
The cause of the fire is under investigation.