Speaking at the scene, station commander Graham Crow said: “This is a prolonged incident and crews will remain on scene for a number of hours.
“Motorists are advised to avoid the area to avoid traffic jams.”
The LFS was called at 12:35 a.m., Mr. Crow said.
Firefighters from Fulham, Wandsworth, Euston, Bethnal Green, Hammersmith, Kensington, Battersea and Chiswick are in attendance.
The cause of the incident is not known at this stage.