Six fire engines and around 40 firefighters tackled a fire at a detached house on Court Road in Eltham.
Part of the ground and first floors of the house were damaged by the fire.
Station Commander Scott Thorpe, who attended the scene, said: "Firefighters rescued six people and three dogs from the fire using a ladder on site. All six people were taken to hospital by London Ambulance Service.
"Firefighters then worked quickly to resuscitate the dogs using animal oxygen therapy kits. The kits contain a set of oxygen masks, which are carried on all frontline fire engines and are designed to safely administer oxygen to small animals suffering from smoke inhalation."
Control Officers took the first of three calls at 0409 and mobilised crews to the scene from Eltham, Lee Green, Sidcup and surrounding fire stations. The fire was extinguished by 0527.
The cause of the fire has been recorded as undetermined.