Verse and prose parables featuring the spider and the fly go back many hundreds of years, and there were certainly examples as far back as the 16th century. This particular version was written by Thomas Hudson (and composed by one "O.H. Normino", which is most likely a pseudonym), an early 19th century performer and songwriter, active in the singing taverns and gentlemen’s supper clubs that influenced early Music Hall. It’s not clear exactly when Hudson first started singing the song, but it was published in his fifth collection of comic songs in 1824 and published by Oliver Dixon [Boston - undated, circa 1815-30].