Six fire engines and around 40 firefighters were called to a fire at a block of flats on Basin Approach in Beckton.
The balcony of a flat on the sixth floor of an eight-storey block was destroyed by the fire and a small part of the flat was damaged. Part of a seventh floor balcony was also damaged. There were no reports of any injuries.
Station Commander Shaun Fox, who was at the scene, said: "Firefighters were faced with a well developed fire on the balcony of a sixth-floor property when they arrived.
"Crews worked hard to quickly bring the fire under control and prevent it spreading inside the flat."
The Brigade's 999 Control Officers took 10 calls to the blaze.
The Brigade's Fire Investigators believe the fire was caused by the unsafe disposal of a cigarette.
A London Fire Brigade spokesperson said: "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.
"If you don't, you risk causing a fire which could not only destroy your home, but also cost you your life."
The Brigade was called at 1159 and the fire was under control by 1249. Fire crews from East Ham, Barking, Plaistow, Stratford and Dagenham fire stations were at the scene.