The copy of the song in 'Northumbrian Minstrelsy', was the first to appear with music. The text and tune there is that given on my website, and the tune is correct (by definition) for the text given there. This copy indicates the chorus starting 'Through by" after each verse. So regardless of what's in Bell's 'Rhymes of the Northern Bards' or Bell's manuscripts, we don't have chorus and verse switched with respect to the two halves of the tune.