The London Fire Brigade said the fire is on Tunnel Avenue in Greenwich, near the O2 arena, and added that one man has been rescued.
"Firefighters wearing breathing apparatus rescued a man who has been taken to hospital by ambulance," said a Brigade spokesperson.
"This is a large fire and the smoke could be seen from across London, meaning our 999 control officers took over 50 emergency calls.
"Our firefighters are making steady progress but they will be at the scene for the rest of the day, and possibly into the evening so please try and avoid the area if possible.
"We are advising people living in the area to keep their doors and windows closed as the fire is producing a lot of smoke."
The fire service said a large part of the ground floor of a nightclub and part of the first floor is alight, and an industrial warehouse is completely alight, while a scrap paper processing yard containing a number of outbuildings is also partly alight.
The Brigade also said: "Some gas cylinders are involved in the fire and as cylinders can explode when exposed to heat a safety cordon has been set up."
According to Twitter users, the fire is at the Studio 338 nightclub in the area.
Studio 338 on fire...sad times 🔥🔥#studio33— Matt Rich (@mattrichdj) August 8, 2016
Smoke from the blaze can be seen from miles away.
From Greenwich pic.twitter.com/4EGhrgWTsq— 🏃♂️ Marco 🇪🇺 (@MarcoCasualty) August 8, 2016