Six fire engines and around 40 firefighters were called to a flat fire on Chadwick Way in Thamesmead.
A first floor flat in a three-storey block was destroyed by the blaze and part of a second floor flat was also damaged. Four people left the building before the Brigade arrived. A man and two women were taken to hospital by London Ambulance Service crews.
Station Commander Lisa King, who was at the scene, said: "Crews were faced with a very well developed fire when they arrived and worked hard to bring the blaze under control.
"There were a lot of possessions and clutter in the property which made it challenging for firefighters.
"Hoarding means exit routes can become blocked, making safe evacuation more difficult.
"Fires can also spread much faster, especially when there are flammable items such as newspapers or cardboard."
The Brigade was called at 0757 and the fire was under control by 0901. Fire crews from Plumstead, Erith, Bexley and East Greenwich fire stations were at the scene.
The fire has been recorded as accidental and is believed to have been caused by an electrical fault.