My guess whilst reading Night Watch (one of Pratchett's most brilliant, IMHO) was that he made it his own song- it's clearly not in 3/4 time, as I "hear" it, and has many more verses than teh "augustine" ones above. I've been hoping someone would come up with a tune for it, but have expected that it would be a new one.
But what do I know? Maybe it is really an oldie.