The above posts have it about right - Heston is now under the M4 services and the Parkway Trading Estate - the main road leading into the latter is still called Aerodrome Rd. Some remnants still exist as part of the trading estate.
Heathrow was developed from Fairy's Great Western Aerodrome - originally it was going to be a bomber base ( I think) but by the time construction was advanced enough for use, the war was drawing to a conclusion and it was clearly not needed for offensive operations, and instead was designated as the new London Airport.
Well, it seems I had it close:
This is an interesting twist -
http://www.heathrow-airport-parking-...throw-history/