My guess was the tune was named after a gentlemen's foxhunting and boozing club, as with the well-known tune "The Caledonian Hunt's Delight".

Something Google isn't being very helpful with: where is the relevant Maxfield? There's a small place near Weston-Super-Mare, and I find references to a Lord Maxfield from the 18th century, but that village is surely too small to have a barony. Where did Lord Maxfield get his title from? - chances are any hunt named after him will have ridden and socialized near there. But I can't see any connection between the name and the Manchester area.