_melisande_, I didn't find the bit yet in the BBC Holmes radio plays where Watson sings the policeman song from Pirates of Penzance, but I checked the part where I remember him singing, and he's singing "Then is the ghost's high-noon" from Ruddigore. Appropriately enough, this is in Hound of the Baskervilles XD Watson loves Gilbert and Sullivan, all right!
I wish I could remember the other story he sings in! Oh well, I'm sure one of us will come across it eventually ^_^