Here's a song by the actual Doctor himself. Yes, Jon Petwee put out his own record in which he "sings" over the main theme music - although "sing" is a bit of a stretch here. The song was first released in 1972 and the theme arrangement was made by Frazer Hines, suggesting that they clearly they didn't learn from his previous Doctor Who musical endeavours. Maybe they just wanted to give him a second chance, and he didn't do too badly, really. Its B-side, Pure Mystery, another spoken-word "song" by Pertwee, had no connection to Doctor Who whatsoever but it's still worth a listen if you like that sort of thing.