Air 67 in The Beggar's Opera is the "Pudding Pies" variant, not exactly the same as the 16th century air.

"Daphne" bears some resemblance to "Greensleeves". A piece called "A Gigg" in The Fitzwilliam Virginal Book, II.237, also has some similiarities. But differences are also clear from the second bar or so:

"Daphne":
Em B Em
When Daphne from fair Phoebus did fly

"Greensleeves":
Em D
Alas my love you do me wrong

In one of the 16th-century references to "Greensleeves" is it designated a "new tune" ? Or not ?