Though Messerschmidt attributes this to Arthur Sullivan, it exists in two collections (see below). In one it is anonymous, but in the other, it is attributed to Hartnett; neither attributes it to Sullivan. Further, both consider it a reel -- "hornpipe" is not in the title of either.
Also published in 1903 in Music of Ireland (O'Neill, Francis) (Chicago: Lyon & Healy), p.285, no.1547, attributed to "Hartnett" (no first name given.
"Hartnett" might not be a composer, just the source where O'Neill picked up the tune. Compare to this tunearch.org set of notes for "Curse the Laws that Gave Me Cause" -- it says "Source for notated version: 'Hartnett' [O'Neill], referring to Chicago police sergeant Michael Hartnett, an Irish dancer originally from the Kerry/Cork/Limerick border region." Though that is a different work, it calls into question whether Hartnett was a composer or merely a source where O'Neill collected some of the tunes in his collection.