If Doctor Who had done a musical episode back in the early 1980s, it might have looked a bit like this. Producer John Nathan-Turner made the cast perform a yearly Cinderella pantomime, and here's one of the numbers.
Yes, it's the Fifth Doctor, Peter Davison, and his then-wife, Sandra Dickinson, doing a number from Cinderella to advertise their holiday pantomime appearance. (For the non-aficionados out there, pantomime is sort of very silly musical comedy aimed at kids, and has nothing to do with mime or French people whatsoever.) This bit appears on the "Enlightenment" DVD, out recently in the U.S., and is a tantalizing glimpse of Davison dancing and singing.