London Fire Brigade said 20% of the basement and kitchen in the building, in Gerrard Place, which houses a restaurant and flats, was alight.
Witnesses in the area described seeing thick smoke billowing from the building.
Firefighters are using two hoses, breathing apparatus and a thermal camera to fight the blaze.
London Ambulance Service said no one was injured or had required treatment as yet.
Police are also at the scene.