Kev
I wouldn't hold out much hope of getting to Heathrow, busiest airport in world = busiest tower in world. You can't fly there as a PPL, so it wouldn't be of any use to you as a learning experience. Better to try and contact your nearest GA/PPL operations airport. Brum is leading the way as far as NATS operated towers go, but others will surely follow. You will learn far more from a smaller place with flocks of Cessnas and Pipers etc than you will at an airport with only commercial IFR traffic.
Once upon a time, I had a signature......
edited for kak spelling