Ten fire engines and around 70 firefighters were called to a fire on Richmond Road in East Twickenham.
The fire involved a three-storey mixed-use building, made up of a shop on the ground floor and flats above. The roof and second floor was damaged along with part of the first floor and ground floor. An outbuilding was also destroyed by fire.
One man was taken to hospital by London Ambulance Service.
The fire was producing a large amount of smoke and people in the area were advised to keep windows and doors closed.
The Brigade received the first of 34 calls at 1638 and Control Officers mobilised crews from Richmond, Twickenham, Chiswick, Acton and surrounding fire stations to the scene. A 32-metre turntable ladder from Clapham Fire Station was also in attendance and used as a water tower to help extinguish the fire from above. The fire was brought under control by 1820.
The fire is believed to have been caused by the unsafe disposal of smoking materials near a timber storage shed.
A London Fire Brigade spokesperson said: "If you smoke it is vitally important you stub it right out, preferably in an ashtray.
"Always ensure your cigarette is completely out when you’ve finished smoking it. If you don’t, you risk causing a fire as you don’t know what it may land on which could potentially start a fire."