Let me explain: the Cumbrian fiddler William Irwin(19th century) had a son, Edwin, who wrote an account of his dad's activities. His dad was taught fiddle by a famous Keswick fiddler, Gillespie(Christian name unknown to me), in about 1820. Now Edwin said that his dad reckoned he wasnt the world's greatest fiddler, and that his teacher Gillespie in particular was much better at playing "Due Mungo" than he was.
So, we can place a tune called Due Mungo in Cumbria in the early 19th century. but what does the title refer to? Mungo was a saint, well known in Cumbria and Scotland, but was also a Christian name. Welsh(or a variant of it) was the language in Cumbria in the time of Mungo, and lasted till maybe the 1300's in some remote parts. So it's probably a very long shot, but just barely possible, that the Welsh language was where I should look to make sense of this peculiar title "Due Mungo". What I dont know is whether Edwin was writing his father's pronunciation down, or his spelling. hence my wondering whether it's pronounced due or possibly dewy.