John Bell gives 2 versions.
In his Rhymes of Northern Bards (1812) p229 'The Jolly Parson' 'Mack' has morphed into 'Moff'
And in Harker JB's Song Collection p143 it has been localised as 'The Parson of Bywell' (Doctor Mews) 'founded upon facts'. Harker notes 'this version probably came to hand just after 'Rhymes' went to press'.
There were lots of these 'Jolly' parsons in the late 18th/early 19th centuries. Even as late as the 1860s they were still being celebrated in song, thus 'Fine Hunting Day'