Ten fire engines and around 80 firefighters tackled a roof fire in a block of flats on Hadleigh Close in Bethnal Green.
The roof of the building was destroyed in the blaze.
Station Commander Paul Morgan, who was at the scene, said: "Brigade Control took twenty-five 999 calls to the visible blaze. One of those callers was trapped inside the property and unable to escape due to fire, heat and smoke.
"They were given vital fire survival guidance information before fire crews arrived. Two women were rescued from a fourth floor flat via a 13.5 metre ladder.
"A man and a woman were also rescued by firefighters via an internal staircase. The man was taken to hospital as a precaution by London Ambulance Service crews.
"Two adults and a child left the flat where the fire is believed to have started before firefighters arrived. Over 100 residents self evacuated from the property."
Thirty flats were affected by the blaze and the local housing agency worked to rehouse residents.
The Brigade's Fire Investigation team believe the fire was accidental and was caused by the unsafe disposal of a cigarette, which caught light to fibreglass framework covering pipes and spread to the roof.
A London Fire Brigade spokesperson said: "Fires caused by smoking materials including cigarettes, roll-ups, cigars and pipes, result in more deaths than any other type of fire. Stub cigarettes out properly and always dispose of them carefully.
"Make sure smoking materials are cold before emptying ashtrays. Preferably wet stubs before throwing them into a bin.”
The Brigade was called at 0328 and the fire was under control by 0539. Firefighters from Bethnal Green, Whitechapel, Shadwell, Shoreditch, Dowgate, Homerton, Soho, Islington and Stratford fire stations were at the scene.