Part of a three-roomed first floor flat in a three-storey residential building was damaged by the fire. One woman suffering from smoke inhalation was led to safety before the Brigade arrived and was treated at the scene by London Ambulance Service crews.
The fire is believed to have been accidental and 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 2.28pm and the fire was under control at 3.10pm. Three fire engines and around 15 firefighters from Erith, Plumstead and Lee Green fire stations attended the scene.