There doesn't seem to be historical evidence of any song set to the tune (though no doubt people who can't leave well alone will have been writing them by the bucketload in recent years since the tune re-surfaced). Simpson (The British Broadside Ballad and Its Music, 467) refers to a Stationer's Register entry of Dec 28, 1591, for "the Thirde and last parte of Kempes Jigge", but only as -perhaps- "a trace of a sequel" to an earlier dramatic jig which may in turn have some connection to the ballad of Lord Willoughby (the tune for which was also known as Rowland and, in the Netherlands, Soet soet Robbertgen).