"King of the Fairies" (in Gaelic Rí na Sideog) appears to be derived from a Jacobite tune called "Bonny Charlie" appearing in many 18th century Scots and Northern English publications, such as Aird (1783). "King William of Orange" is a British title for the melody.
This a hornpipe version of "Scollay's Reel" and the two go well together in a medley.
Traditional set dances are done in the faster tempos ("fast jig", "fast hornpipe").
There are five traditional sets:
"St. Patricks Day" (treble jig),
"The Blackbird" (hornpipe),
"Job of Journeywork" (hornpipe),
"The Garden of Daisies" (hornpipe), and
"King of the Fairies" (hornpipe).
I learned this from the Irish Rovers who added words. I always thought that the tune was far too interesting to be obscured by words. I later learned a more traditional version from print.