Fifteen fire engines and 97 firefighters are currently at the scene trying to extinguish the blaze, London’s Fire Brigade has reported.
Transport for London said roads have been closed as emergency services deal with the incident.
A London Fire Brigade spokesman said: "Fifteen fire engines and 97 firefighters and officers have been called to a visible fire in William Street in Knightsbridge.
"The Brigade's 999 control officers have taken more than 35 calls to the fire, which is producing a lot of smoke.
"The Brigade was called at 1555. Fire crews from Chelsea, Kensington, Hammersmith, Battersea and other surrounding fire stations are at the scene.
"The cause of the fire is not known at this stage."