Five fire engines and around 35 firefighters were called to a fire at a flat on Greens End in Woolwich.
A small part of a flat on the ninth floor was damaged by the fire. There were no reports of any injuries.
The Brigade was called at 1442 and the fire was under control by 1544. Fire crews from Greenwich, Bexley, Poplar, Lewisham and New Cross fire stations attended the scene.
The Brigade’s fire investigators believe the cause of the fire was accidental and was due to a fault in the heating element in the heating and ventilation system.