Six fire engines and around 35 firefighters were called to a flat fire on Kale Road in Erith.
Part of a twelfth floor flat was damaged by fire.
Three adults and nine children left the affected flat before the Brigade arrived.
The Brigade was called at 0619 and the fire was under control by 0710. Fire crews from Plumstead, Erith, Bexley and East Greenwich fire stations were at the scene.
The fire is believed to have been accidental and caused by items placed on top of a hob igniting.