Six fire engines and around 40 firefighters were called to a fire at a maisonette on Rhodeswell Road in Limehouse.
Part of a three-roomed maisonette on the third and fourth floor of a six-storey block was damaged by fire.
A woman, two children and a cat left the building before the Brigade arrived. There were no reports of any injuries.
The Brigade was called at 2005 and the incident was over by 2109. Crews from Poplar, Millwall, Shadwell, Whitechapel, Bethnal Green and Shoreditch fire stations were at the scene.
The cause of the fire is under investigation by the Brigade and the Metropolitan Police Service.