The ground floor of the mid-terraced shop was damaged by the fire. Firefighters led three women to safety and another four adults left the flats above before the Brigade arrived. There were no reports of any injuries.
The Brigade was called at 3.522pm and the fire was under control by 5.34pm. Fire crews from Plumstead, Erith, East Greenwich and Bromley fire stations were at the scene.
The fire is believed to have been accidental and caused by a fault within an air conditioning unit.