The London Fire Brigade (LFB) have sent four fire engines to the scene of the blaze on the High Street in Teddington on Sunday (September 11) afternoon.
LFB said they were called just after 3.30pm to reports of a fire at a restaurant and dwellings of one and three floors.
Video footage taken by Joanne Muhammad shows thick black smoke rising.
A LFB spokesperson said: "We were called at 3.38pm to a restaurant and dwellings of one and three floors on fire.
"Internal ducting from the ground floor to the first is 50% alight."
Reports on social media site Twitter suggest the fire ignited at Indian Restaurant Prem.
Thick plumes of black smoke were reported to be seen by people enjoying a warm Sunday picnic in Bushy Park.
It is not known whether anyone has been injured.