Four fire engines and around 25 firefighters were called to a fire at a flat on Arboretum Place in Barking.
The balcony of a five-roomed flat on the seventh floor of the 18-storey building was destroyed by the fire and a small part of the flat was damaged.
Firefighters wearing breathing apparatus rescued one woman. Around 60 people left the building before the Brigade arrived. There were no reports of any injuries.
The Brigade was called at 1107 and the fire was under control by 1230. Fire crews from Barking, East Ham and Ilford fire stations attended the scene.