Part of a three-roomed flat on the second floor of the building was partly damaged by the fire. A woman and two children left the property before the Brigade arrived. The woman was treated at the scene for smoke inhalation by London Ambulance Service crews and the two children were taken to hospital.
The Brigade was called at 2.57pm and the fire was under control by 1600. Fire crews from Bethnal Green, Shadwell, Homerton, Poplar and Dowgate fire stations attended the scene.
The cause of the fire will be investigated.