Four fire engines and around 25 firefighters were called to a fire at a seven-storey block of flats on Turner Street in Canning Town.
Two industrial paladin bins were removed from a bin room that was destroyed by the blaze.
Around fifteen people left the building before the Brigade arrived.
The Brigade was called at 1703 and the fire was under control by 1755. Fire crews from Plaistow, Poplar, Millwall and Shadwell fire stations attended the scene.