Ten fire engines and around 70 firefighters were called to a flat fire on New Village Avenue in Tower Hamlets.
A five-roomed flat and a balcony on the eighth floor of the building was destroyed by fire. Part of a balcony on the ninth floor was also damaged by the blaze. Three men left the flat before the Brigade arrived. Firefighters wearing breathing apparatus rescued four people. They were assessed on scene by London Ambulance Service crews and another person was taken to hospital.
The Brigade's 999 Control Officers received 40 calls to the blaze.
Station Commander Matt Williams, who was at the scene, said: "Firefighters evacuated 20 people from the building and rescued four people via an internal staircase.
"One of the Brigade's new 32-metre ladders from Old Kent Road Fire Station was used as a water tower and crews also used drones to provide an aerial view of the incident and increase situational awareness.
"Abbott Road was closed at the A13 junction down to the junction by Blair Street. Firefighters remained on scene throughout the night and we encouraged people to avoid the area whilst crews worked to make the scene safe."
The Brigade was called at 2233 and the fire was under control by 2348. Fire crews from Plaistow, East Ham, Greenwich, Shoreditch and surrounding fire stations attended the scene.
The cause of the fire is under investigation.