I think that the Bucket of Water Song was largely written by Neil Innes (from Bonzo Dog Do Da Band etc etc) and John Gorman (formerly of folk-comedy band Scaffold). It definitely resembles some of their late 1960s stuff!

There was lots of folk-comedy stuff on Tiswas - Jasper Carrott was a presenter in its early days, and you would see Mike Harding, Grumbleweeds, Fred Wedlock, Barron Knights, Roaring Jelly and people like that.