I did this last year in May. Was shown around the centre and the building by a brilliant longtime employee of the airline. He is in charge of the BA heritage and history, and has even taken Queen Elizabeth II on the tour. An amazing gentleman! All the staff were great, too.

You just have to show permission to use the BA bus from T5, but the driver didn't seem to care. An ID or passport is also required, which they will use to give you a pass (according to Jim, it's for VIPs). I'd really recommend this if you are near Heathrow, and have at least half a day to spare. You can't go wrong if you're an aviation enthusiast.