I understand that the melody came from a British drinking song

Voila:
http://www.bcpl.net/~etowner/anacreon.html

no sense to me because the melody is fairly challenging to sing well, and I cannot imagine a bunch of drunks singing it without sounding like a pack of howling hounds
A few drinks make you sing better, as any Irish(wo)man will tell you (Helen? ). It's only when you've really overdone it that you start sounding better to your own ears than you actually sound. And really then it's more a matter of not giving a fig.

Nothing wrong with the odd howl. Where would the Blues be without 'em?