Here are two interesting alternatives to the usual versions we know so well.
This Lavenders Green uses a tune and verses collected by the Reverend Sabine Baring-Gould, while Old King Cole uses the tune that appeared in a book of nursery rhymes called ‘Little Songs of Long Ago, published in 1912.
The author doesn’t tell us where the Old King Cole tune came from, but it sounds like a traditional tune to us – though of course it could be a tune of the time carefully composed to sound like something older.