Four fire engines and around 25 firefighters tackled a flat fire on Titmuss Avenue in Thamesmead.
Half of a three-roomed flat on the first floor of a residential block was damaged by fire. One person left the building before the Brigade arrived and was taken to hospital by London Ambulance Service crews.
The fire is believed to have been accidental and caused by a halogen table lamp which set nearby clothing alight.
A London Fire Brigade spokesperson said: "Lightbulbs can get incredibly hot and can set fire to combustible materials.
"It's important to keep them on stable surfaces, away from anything that might catch fire such as books, clothing, sheets and curtains.”
The Brigade was called at 0506 and the fire was under control by 0624. Fire crews from Plumstead, Erith, Bexley and East Greenwich fire stations attended the scene.