I suspect Vaughn Williams used the tune for the English folk song "The Princess Royal". Another "Princess Royal" is in Walsh's first book of "The Compleat Country Dancing Master", 1731 (not the same as the 1718 one, although there's some overlapping), and in his 3rd book, 1735 is "Princess Royal the New Way". This latter is Carolan's "Miss MacDermott" and is the one that Wm. Shield used for the song "The Arethusa" (a 2nd song of that title), and not that for the English folksong.