The London Fire Brigade (LFB) said one of its 64-metre turntable ladders – the highest firefighting ladder in Europe – attended the scene on Grantham Road in Manor Park, to deal with the fire in a 15-storey building.
LFB said it was called at 2.47pm and about 60 people left the building before firefighters arrived.
Half of a flat on the 13th floor and the whole of a flat on the 14th floor was damaged by fire.
Fire crews from Ilford, Stratford, Leytonstone, Plaistow, Dagenham and surrounding fire stations are at the scene, LFB said.
LFB’s 999 control officers took 50 calls about the blaze.
The cause of the fire is not yet known.