Eight fire engines and around 60 firefighters tackled a fire in a block of flats on Cassilis Road on Isle of Dogs.
Part of a seventh floor flat was damaged by fire.
Station Commander Shaun Fox who was at the scene said:
"First crews worked very hard and contained the fire to the flat of origin. Two adults left the affected property, uninjured, before we arrived. A further 40 people from surrounding flats self evacuated."
The Brigade's fire investigators found the cause of the fire was accidental. A candle was lit with combustible material close by.
A London Fire Brigade spokesperson said: "Candles are one of the most common causes of fire in the home.
"We recommend you swap your candles for flameless, LED candles. They are safer as you can leave them unattended. You don't have to worry about them being knocked over or falling asleep while they are on."
The Brigade was called at 1948 and the fire was under control by 2044. Firefighters from Millwall, Poplar, Shadwell, Whitechapel, Bethnal Green, Plaistow, Dowgate and Dockhead fire stations were at the scene.