Drones were used to provide aerial views of the building as firefighters used large turntable ladders to dampen the flames from above.
Large capacity, long distance hose lines were also used, LFB said.
LFB station commander Wayne Bloomfield, who was at the scene, said: “Firefighters have worked hard overnight and have now fully extinguished this fire.
“At its height, the fire involved a large amount of refuse and the roof of a warehouse unit.
“A van and a car were also destroyed by the fire. One man was treated on scene by London Ambulance Service.”