Five fire engines also attended the fire on Upper Richmond Road.
It broke out in an eight-storey mixed-use building made up of homes and offices.
A tumble dryer in an office on the third floor was destroyed by the fire.
The Brigade was called at 9pm and crews from Fulham, Battersea, Hammersmith, Richmond and Clapham fire stations attended the scene.
The cause of the fire is under investigation.