Eight fire engines and around 60 firefighters were called to a flat fire on Jupp Road West in Stratford.
Part of a flat on the fifth floor was damaged by the blaze. Two people left the property before the Brigade arrived. They were both taken to hospital by London Ambulance Service crews.
Around 40 people self-evacuated the block while a number of residents stayed in their unaffected flats.
The Brigade's Fire Investigators believe the fire was accidental and caused by an unattended candle igniting items on a bedside table.
A London Fire Brigade spokesperson said: "Candles are one of the most common causes of fires in the home and you should be careful when using them.
"This is a reminder to never leave candles unattended and keep them away from anything that could catch fire such as curtains, furniture or clothes.
"We recommend swapping traditional candles for LED flameless ones as they are much safer, but if you do use real candles, follow our simple safety tips."
The Brigade was called at 2129 and the fire was under control by 2242. Fire crews from Stratford, Leytonstone, Plaistow, Leyton, Homerton, Millwall and East Ham fire stations were at the scene.