Six fire engines and around 40 firefighters were called to a fire at a farm on North Cray Road in Bexley.
Four horseboxes were destroyed by fire and a stack of baled of hay and wood chippings were damaged by the blaze. There were no reports of any injuries.
Group Commander Clinton Walsh, who was at the scene said: "Crews will remain on scene damping down deep seated pockets of fire throughout the day.
"Road closures are in place whilst crews work to make the scene safe, so we urge locals to avoid the area.
"Thankfully, there were no injuries and no animals were hurt."
The Brigade was called at 0710 and the fire was under control by 0847. Fire crews from Bexley, Sidcup, Erith, East Greenwich and Eltham fire stations are at the scene.
The Brigade's Fire Investigators believe the fire was accidental.