A candle is believed to have caused a flat fire on Braintree Road in Dagenham.
Half of a flat on the first floor was damaged by fire and the rest of the flat was damaged by smoke.
The Brigade's Fire Investigation team believe the fire was accidental and that the most likely cause was a candle falling over and igniting the carpet or nearby furniture.
Station manager Jeremy Barker, who was at the scene, said: "Crews worked hard to contain the fire to the flat of origin and brought the fire under control quickly.
"Firefighters rescued one man from a flat on the second floor and a woman and two children from a neighbouring flat on the second floor by ladder.
"Thankfully due to the quick work by crews, there were no injuries but all four people rescued have been treated at the scene by London Ambulance Service for smoke inhalation as a precaution."
One adult and two children also left the building before the arrival of the Brigade.
The Brigade's 999 Control Officers took 24 calls to the fire.
The Brigade was called at 1532 and the fire was under control at 1628. Ten fire engines and around 70 firefighters crews from Ilford, Hornchurch, Dagenham and other surrounding fire stations attended the scene.