The machines have been flown so close to planes near the airport on occasions that the air crew who reported them were able to see what colour they were.
Officers have warned people they face up to six months in prison for flying drones irresponsibly, or a life sentence if they are shown to have endangered the safety of an aircraft.
Police, who say Hounslow Heath is a hot spot for drones, have received complaints from air crew on these dates:
- April 8, 10.25am: Heston Road, Heston
- March 29, 10.22am: Wraysbury Close, Hounslow
- March 28, 8.48pm: Chiswick High Road, Chiswick
- March 13, 12pm: near Hounslow Heath Golf Course
- March 8, 10.23am: near Osterley Tube station
- February 22, 4.33pm: near Hounslow Heath Golf Course
Anyone caught flying an unmanned aircraft above 400ft or beyond their eyeline can be convicted under the air navigation order 2009, which carries a maximum sentence of six months' imprisonment.
Should their actions cause a pilot to take evasive action, they could be charged with endangering an aircraft and jailed for life.
'It could be your loved ones whose lives you are endangering'
A spokeswoman for Hounslow police said: "We're on the flight paths to Heathrow so people flying drones should be sensible about how they do so and make sure they are operating within the law.
"It could be your loved ones on a plane above whose lives you are endangering."
getwestlondon reported earlier this year how an illegally operated drone came within metres of a plane landing at Heathrow .
Pilots are also facing the danger of potentially blinding lasers being deliberately shone at planes around Heathrow , with recorded incidents having rocketed recently.
A Heathrow spokeswoman said: "The unauthorised use of unmanned aerial vehicles in proximity to an airfield is both irresponsible and illegal.
"Heathrow's top priority is the safety of our passengers and colleagues. The CAA recently published revised guidelines on the use of UAVs and we will continue to work with them and other partners to ensure that any violation of airspace rules is fully prosecuted."
If you see a drone being flown irresponsibly, you can report it by calling the non-emergency police number 101.