Four fire engines and around 25 firefighters were called to a fire at a flat on Lewisham Road in Greenwich.
Part of a four-roomed flat on the eighth floor of a 13-storey block was damaged by the fire. Firefighters led one person to safety from the affected flat, via an internal staircase. A further 30 people left the building before the Brigade arrived. There were no reports of any injuries.
The Brigade was called at 1252 and the fire was under control by 1331. Fire crews from Lewisham, Greenwich, Deptford and Lee Green fire stations were at the scene.
The Brigade's Fire Investigation team believe the fire was accidental and caused by a fault in a washing machine.