Six fire engines and around 40 firefighters were called to a fire at a detached house converted into flats on Lingards Road in Hither Green.
The roof was destroyed by the fire and half of the first floor was damaged. Two people left the building before the Brigade arrived. One man was treated on scene by London Ambulance Service crews suffering smoke inhalation and taken to hospital.
The fire was discovered by a neighbour who and saw smoke coming from the roof and called 999.
A London Fire Brigade spokesperson said: “There were smoke alarms in this property, but they were not fitted properly and failed to alert the residents to the fire.
"We urge people to have working smoke alarms on every level of your home and to test them regularly. Smoke alarms will give the earliest possible warning if a fire breaks out in your home.
"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 and the bathroom. They should be tested regularly."
The Brigade's 999 Control Officers took 13 calls to the fire.
The Brigade was called at 1135 and the fire was under control by 1323. Fire crews from Lee Green, Greenwich, Forest Hill, Deptford, New Cross and East Greenwich fire stations attended the scene.
The cause of the fire has been recorded as undetermined.