If Harry Christophers doesn't know who wrote "Greensleeves" (he's sure it wasn't Henry the Eighth, though), then we can be quite sure it's an E. trad./English traditional folk song: as used by John Gay in the folk-opera The Beggar's Opera; a record number, apparently, of ice-cream vans; and, I've just learnt, in parody by an Aussie folk-group.