Don't rely on just postcode searches (TW6) or text "Heathrow" since, depending on how you intend to travel there, the listings can throw up wilding different and disparate areas: Hounslow, Hillingdon, Feltham, Drayton: none of which are the airport itself.
If you are arriving at the airport and your chosen amour is in a local (usually Bath Road) hotel, the taxi is a minimum £30 fare despite being only a few minutes away: you may prefer to take the bus (circa 15 mins if one is ready to go) unless time is of the essence.