Absolutely fascinating! Let me see if I have the bones of the origins right now ...

1   The earliest reference to the tune was William Ballet's Lute-Book c1600 [Is the specific publishing date known?] and it was also quoted in John Playford's The English Dancing Master 1651.
2   The lyrics were published (and most likely written) by Robert Cox in his Actæon and Diana, with a Patorall Story of the Nymph Oenone; Followed By the several conceited humors of Bumpkin, the Huntsman. Hobbinal, the Shepherd. Singing Simpkin. And John Swabber, the Sea-man (2nd ed.) 1656. [Is it known whether they were also in the 1st edition and when was that published?]
3   There is no evidence from this to connect morris dancing and maypole dancing or to link it with Staines in Middlesex, West London.
4   The words and lyrics were brought together by William Chappell in his Popular Music of the Olden Time (vol. 1) 1859.

Thanks again!

"Here each batchelor may choose ...!"
Alan