Perhaps not in the folk-song category; but a lot of fun to sing are the catches and glees from Elizabethan times. There were some groups in the 60s that performed them--some with period instruments and some unacompanied. I can't recall the names of the groups; but they used John Feranti frequently as a counter-tenor and they recorded on a cheap lable called "Nonesuch" (I gave away the vinyls before moving to Australia thinking I could replace them any time, sigh.)

Murray