The fire brigade was called to a semi-detached house in Grove Street around 8am on March 26.
When they arrived, one woman had already escaped and was taken to hospital by ambulance.
But another two were rescued by firefighters before also being taken to hospital for treatment.
Most of the first floor was damaged by the fire with pictures showing a blackened window.
The fire is understood to have been started by a lit cigarette which was not put out properly.
25 firefighters and four engines from Deptford, Greenwich, New Cross and Dockhead fire stations managed to put the blaze out just before 10am.
One of the Brigade’s 32-metre turntable ladders was used to help fight the fire from above.
A London Fire Brigade spokesperson said: “If you smoke it’s vitally important you stub it right out, preferably in an ashtray.
“Always ensure your cigarette is completely out when you’ve finished smoking it. If you don’t, you risk causing a fire.”
