Four fire engines and around 25 firefighters tackled a fire on Prentiss Court in Charlton.
A flat on the first-floor of a two-storey block of flats was destroyed by fire. One man left the flat before firefighters arrived. He was taken to hospital by London Ambulance Service crews suffering from smoke inhalation.
The fire is believed to have been caused by the unsafe disposal of smoking materials.
A London Fire Brigade spokesperson said: "We'd rather you didn't smoke at all, but if you are a smoker, it's absolutely vital you ensure your cigarette is completely out when you've finished smoking it.
"If you don't, you risk causing a fire which could not only destroy properties but also cost you your life."
The Brigade was called at 0755 and the fire was brought under control by 0919. Crews from Plumstead, Eltham and Lewisham fire stations attended the scene.