Four fire engines and around 25 firefighters tackled the blaze in Marsala Road just before 1.45am yesterday (May 21).
Part of the buildings ground floor was damaged in the fire.
The adults and child were rescued from the house before being assessed at the scene for smoke inhalation.
They were taken to hospital for further treatment shortly after.
Crews from Lewisham, Greenwich, Lee Green and surrounding fire stations attended.
Firefighters were able to bring the fire under control just before 2.45am.
The cause of the fire is under investigation by the London Fire Brigade.
