Five fire engines and around 35 firefighters were called to a fire at a block of flats on Branch Road in Limehouse.
Part of an electrical intake cupboard on the sixth floor of the building was damaged by fire. There were no reports of any injuries.
The alarm was raised by a resident who could smell burning and saw smoke in the corridor.
Station Commander Robbie Robertson, who was at the scene, said: “On arrival, crews were faced with smoke coming from an electrical intake cupboard in a communal corridor.
“Firefighters assisted around 20 people from the building to safety and worked quickly to prevent the fire from spreading to neighbouring properties.”
The Brigade was called at 2224 and the fire was under control by 2352. Fire crews from Shadwell, Poplar, Whitechapel, Millwall and Bethnal Green fire stations attended the scene.
The Brigade’s Fire Investigators believe the fire was caused by an electrical fault.