In my days at Heathrow, back in the eighties, we once had a posse of light singles arrive, park and depart a while later. Believe me, this was considered by all on the ground as a big imposition - we felt we had to be there for the flights actually scheduled - many of the long-haul flights of course bridge either Christmas Eve or Boxing Day. We were operating on a 'skeleton' staff basis to give as many as possible the day with their families. Don't get me wrong, I was then and remain a keen GA pilot, but it just seems selfish to carry out this sort of activity on the one day a year when all but essential ops are suspended to give everyone a little bit of peace and goodwill to our fellows.
Many GA airfields close for the day, out of courtesy to their neighbours and quite right too.
Gatwick is expecting around 200 movements on Christmas Day this year so it's unlikely you'll get access to the approach. Helicopters are normally accommodated crossing the threshold, but they can hold conveniently. The trial doing the same with fixed wing last year failed and hasn't been repeated. You'll probably get a routing far enough away from the aerodrome to make the experience not very interesting.
Cheers,
The Odd One