The fire was extremely visible and the Brigade’s 999 control took 34 calls to the blaze.
The fire badly damaged a flat on the seventh floor.
Around 80 people left the building before the Brigade arrived. There were no reports of any injuries.
The Brigade was called at 0012 and the fire is under control by 0126. Fire crews from Plaistow, Millwall, East Ham, Stratford, Shadwell, East Greenwich, Whitechapel and Barking fire stations attended the scene. The cause of the fire is under investigation.