Chappell PMOT gives the earlier references to the ballad opera The Jovial Crew (1731) using the air as Three Merry Men of Kent. You can see that here: The Jovial Crew - And he that will not merry, merry be.

His earlier reference is to Folly In Print (1667) as Three Merry Boyes of Kent. I can't see that (it's online at U,Mich if you have access), but you can see an index entry for it here: Poems in Folly In Print: Poem Title: Three merry Boyes of Kent. To the Tune of an old song, beginning thus I rode from England into France. Or to the Tune of Sir John Sucklings Ballad.

Mick