Six fire engines and around 40 firefighters were called to a fire at a block of flats on Hallywell Crescent in Beckton.
A block of flats of three and four storeys was involved and part of the roof and loft space at third floor level was damaged by the blaze. Around 30 people left the building before the Brigade arrived. There were no reports of any injuries.
The Brigade's Fire Investigation team believe the fire was accidental and caused by the unsafe disposal of smoking materials.
Station Officer Scott Fitzearle, who was at the scene, said: "Crews worked hard to tackle the fire and stop it spreading further into the roof voids of the building.
"We believe the fire had been smouldering for some time as there was a build up of discarded cigarettes on the roof.
"We’d rather you didn’t smoke at all, but if you are a smoker, it’s absolutely vital you ensure your cigarette is completely out when you’ve finished smoking it.
"It's dangerous to throw cigarettes out of windows or off balconies as they can easily catch light to items below and start a serious fire.
“By not disposing of your cigarettes properly, you risk causing a fire which could not only destroy your home, but also cost you your life.”
The Brigade was called at 2138 and the fire was under control by 0156. Fire crews from East Ham, Plaistow, Barking, Dagenham and Poplar fire stations were at the scene.