Although the song may have become 'universal' in that you could just change the town name, I suspect that, orginally, it was written about Howden because, as I mentioned earlier, itwas the biggest horse fair at the beginning of the 19th century but ended around the early 1840s when the Hull to Selby railway line was built (1837). The song is definitely about a horse fair and was probably written before 1840.
It's also interesting that the song appears to originate in Brigg, which, of course, had its own fair and is just across the Humber from Howden. So, there may be an element of rivalry here, with Lincolnshire (Brigg) residents poking fun at a Yorkshire (Howden) institution. The Yorkshire/Lancashire rivalry is still alive and well, but maybe there was a Yorkshire/Lincolnshire rivalry as well, although this doesn't exist so much today.