Four fire engines and 21 firefighters and officers were called to a fire at a block of flats in Paget Rise, Plumstead.
A small part of a three-roomed flat on the lower ground floor was damaged by fire. There were no working smoke alarms in the flat.
A man was rescued from the lower ground floor by fire crews wearing breathing apparatus. He was treated at the scene for smoke inhalation before being taken to hospital by London Ambulance Service crews.
Another nine people were also led to safety by firefighters.
A London Fire Brigade spokesperson said: "Homes need multiple and linked smoke alarms or you won’t be properly covered. Ideal spots for smoke alarms include rooms where you leave electrical equipment running like satellite boxes, computers or heaters; any room where you smoke, and anywhere you charge your mobile or laptop.
“As a minimum you should have smoke alarms on every floor - in the hallways and the rooms you use the most, plus a heat alarm in the kitchen. They should be linked together and tested regularly."
The Brigade was called at 0009 and the fire was under control at 0122. Fire crews from Plumstead, Eltham and East Greenwich fire stations attended the scene.
The cause of the fire is under investigation.