A few points from previous posts on this thread:
(1) Regardless of legality or otherwise (please bear with me, Madam Moderator) surely the real question is one of decency and consideration for others in a delicate situation.
(2) Yes, SylviaAnn, WW1 records including medical details may be seen at Kew, although some are missing, and many are just indecipherable, so don't raise your hopes too much. Nevertheless Kew is a wonderful place - IMHO the acceptable face of government. (Incidentally, my wife's very unassuming grandfather turned out to have contracted VD during WW1, and to have taken part in a mutiny in 1919!)
(3) Suey, I think the prog gave a misleading impression. An individual soldier's record will not normally be available at a Regimental Museum, unless he was really notable in some way. Also bear in mind that they are often staffed by volunteers or part time folk who just would not have the time to respond to many queries.
(4) Yes, Carol, we've all suffered from family folklore!. And I well remember Walker's bitter (terrible stuff it was too). Surely the connection with the splendid Walker Art Gallery is that it was initially funded by the wealthy brewer?