Eight fire engines were sent to the scene after flames engulfed a shop with flats above at 1.10pm today (July 22).
The entire ground floor, first floor, and roof are alight, and part of the roof of a neighbouring building has also caught fire.
Station Commander Steve Howlett, who is at the scene, said: “This is a very visible fire which is producing a significant amount of smoke in the area.
“Please keep your windows and doors closed if you live or work in the vicinity.”
A 32-metre turntable ladder is being used as a water tower to tackle the flames from above.
Blackfen Road has been closed and some local bus routes are affected.
Crews from Eltham, Lee Green, Sidcup, East Greenwich and other surrounding fire stations are responding after the brigade received nearly 30 emergency calls.
The cause of the fire is not yet known.