Four fire engines and around 25 firefighters were called to heavy smoke coming from a block of flats on Sherwood Gardens in Millwall.
Several flats and the basement suffered smoke damage. Around 20 people were led to safety by firefighters wearing breathing apparatus.
The smoke is believed to have been caused by overheating hydraulic oil in a lift.
The Brigade was called at 0732 and the incident was over for firefighters at 0856.
Firefighters from Millwall, Poplar, Shadwell and Whitechapel fire stations attended the scene.