I don't know of any songs with tunes of that description prior to the 16th century. Songs earlier yes but not with their tunes (Robbins' 'Secular Lyrics of the 14th and 15th Century', Chambers and Sidgwick's 'Early Engish Lyrics', There's also a newer compilation I have but can't locat at the moment). For 16th century ones most that I've seen are on my website in Scarce Songs 1, with tunes as ABCs. You might try the SCA Minstrel website, too. The earliest that I can recall is the "Friar and the Nun" which might go back to about 1500. Then there's "Watkins Ale" and "Carman's Whistle", both apparently based on the lost "Maukin was a Country Maid", which survives in 17th and 18th century versions.
www.erols.com/olsonw