Five fire engines and around 35 firefighters were called to a flat fire on Burcham Street in Poplar.
Part of a flat on the fifth floor of the building was damaged by fire. Around 30 people left the building before the Brigade arrived. There were no reports of any injuries.
Control Officers gave fire survival guidance to residents inside their flats on how to stay safe before firefighters arrived.
The Brigade was called at 1302 and the fire was under control by 1351. Fire crews from Millwall, Shadwell, Whitechapel, Plaistow and Poplar fire stations attended the scene.
The cause of the fire is under investigation.