GCC - won't be that way on the 24th unfortunately.
I would suggest to anyone wanting to go:
Don't drive. Really no - the best use for the inner roads will be for spectators, potentially forcing essential airport traffic further out. Spectator vehicles in the area will frustrate things for everyone - the people coming to watch, those who've come to catch a flight, and the normal stuff that has to shuttle around to make the airport work.
Instead, take the tube to Hatton Cross and work it out from there (theoretically you could take a bus, but plan on a 30 minute+ walk round to the perimeter by the North runway. Definitely skip the idea of going to the terminals - by tube, heathrow express or whatever - they're pretty rubbish for views anyway, and the plod will be out in force to stop it going silly.
Expect the view from the perimeter to be a bit limited. The screens on the fence will be problematic, but you may still get to see some action before the flare and roll. The earliest of birds might get a seat in some limited grandstand seating, but the as-likely limited scale of it (or any special arrangements like tickets) is not public domain yet.
If you want a convenient 30 mins of nice aircraft views, then BBC2 is probably the place to be.
But if - like many of us - you really feel you have to be there, then set the video recorder and get down there. You may walk away feeling like you've gone travelled afar to watch your favourite team lose the championship, but there isn't an alternative. And who knows, the Met + BAA just might make it work, albeit crudely, for the spectators taking their chance.