There are a number of places, however, only one legal one
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The Queens Building has the spectators viewing area, which is next to terminal 2 in the central area, however, I have not been there for a while and last time I was there, there was rather a lot of construction work going on, blocking out some of the good views!
Terminal 3 cark park, on the top floor is pretty good for views of the north side of the airfield, overlooking 27R/09L runway. There are also some good spots around the airport, ESSO petrol station on the south perimeter, good for when 09R is in use, and at the end of runways 27L (hatton cross) and 27R over where BA maintenance is when they are landing to the west. I must point out that it does stipulate you cannot spectate in these areas, but I am sure you won't get sent to jail
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Hope this helps.