Les Barker has written a lot of parodies on (folk) singers or groups:
Watersons (tune: Waterloo)
Eliza (for Eliza Carthy to the tune of Delilah)
January June (for June Tabor, tune: January Man)
Older than Swarbrick
there's one about Martin Carthy (forgot the title)

Don't forget Orpheus (Orfeo?), a famous old (folk) singer with more than one whole opera devoted to him. Or a musical devoted to ABBA (ah, Wolfgang, that's very far from folk).

Wolfgang