Six fire engines and around 45 firefighters responded to a fire on Western Gateway in Canning Town.
Part of a balcony on the 19th floor, in a block of 20 floors, was damaged by fire. Around 12 people left the building before the Brigade arrived. There are no reports of any injuries.
Control Officers took the first of 9 calls at 0224, and crews had the fire under control by 0335. Firefighters from Shadwell, Plaistow, Millwall and surrounding fire stations attended the scene.
The fire is believed to have been caused by the unsafe disposal of smoking materials.