Never heard The Muffin Man tune used for the Dorset Four Hand - that's got its own tune. We used to use a tune called Grandma's Polka (as I recall - I know a lot of these tunes by ear and by the dance rather than by name!) which starts off very similar to Muffin Man but goes off into its own thing (and the second tune we used was Speed the Plough unless they complained, in which case we played Slow the Plough).