Four fire engines and around 25 firefighters tackled a fire on Selsey Street in Mile End.
Most of a maisonette flat on the ground and first floors of a five-storey building was damaged by fire.
The Brigade's 999 Control Officers received seven calls about the fire.
The Brigade was called at 1302 and the fire was under control by 1403. Crews from Millwall, Stoke Newington, Shadwell and Whitechapel fire stations attended the scene.
The cause of the fire is under investigation.