Six fire engines and around 40 firefighters tackled a fire on New Barn Street in Plaistow.
Half of a balcony on the 20th floor of a 23-storey residential block was damaged by fire. Two adults and one child were rescued before firefighters arrived. They did not require hospital treatment.
The Brigade was called at 0006 and the fire was extinguished by 0148. Crews from Plaistow, Poplar, East Ham and surrounding fire stations attended the scene.
The fire is being treated as accidental.