Stuart Douglas gave an e-mail address for the RT a few posts ago. It's firstname.lastname@example.org . If you can give them a home or e-mail address or phone number for your father, it would be helpful. I'm sure they have developed a level of decorum in situations like these.
I haven't watched the Tenth Planet episodes yet. It's not Tomb. It's not Moonbase 2 or 4. It's not Moonbase 1 but it could be Moonbase 3 based on the soundtrack on the Lost In Time release but I think it very unlikely. I haven't watched the Wheel episodes yet nor have I been able to get a copy of the soundtracks. I haven't managed to get the Invasion episodes or soundtracks yet either. Is that all of them?
After I've watched the other episodes I'll look into it further. It would be great to see Moonbase 3 as the soundtrack was very good. 'Clever, clever, clever.' It's sadly unlikely that my father will have any Doctor Who episodes though. He is a fan of the series but I honestly can't see him paying much for an episode.
Anon, how sure are you that what you saw was a Cybermen episode? I remembered this afternoon that "The Seeds of Death", the second Ice Warriors story, was set partially on the Moon. "Sad" to say, all six episodes are in the archives. Might that have been what you saw? Sorry to be a spoilsport about this.
Or could the story you saw be an episode of the Patrick Troughton story "The Dominators". The Quarks ( square shaped robots, with small feet, and a round head with spikes and what looks like hundreds of washers glued on). Or was what you saw definitely an cybermen episode? Have you yet had time to view any episodes of the Tenth Planet, and the reconstruction of the missing part 4 at the very end of the tape? Something you might want to look into.