Hello Q. I always refer to it as "Let's go a-Huntin'" but there's a problem with this title. Lomax collected another completely different song by the same title. I assume this might be why the song we are disscusing is usually called "Billy Barlow". Also the other Billy Barlow songs were long forgotten by then.
(For good reason because they were always meant to be topical and transient.)
No I have never found a 19th century version of this song and my speculation about a Cowell connection is only that. It's based on a hunch only. There is some circumstantial evidence. If I can ever come up with written confirmation I'll be posting it here and shouting it from the roof-tops. Believe me I've tried.
Cheers, Joy