Firefighters were called to a flat fire on Commercial Road in Limehouse.
Half of a bedroom in a three-roomed flat on the fifth floor of the building was damaged by fire. There were no reports of any injuries.
The fire is believed to have been accidental and caused by a lamp that was placed too close to a curtain.
A London Fire Brigade spokesperson said: "Lightbulbs can get incredibly hot and set fire to combustible materials.
"It's important to keep them well away from anything that might catch fire such as books, paper, sheets and curtains.”
The Brigade was called at 0740 and the fire was under control by 0821. Five fire engines and around 35 firefighters from Shadwell, Millwall, Whitechapel, Bethnal Green and Poplar fire stations attended the scene.