A suggestion is that it is a corruption of "The Macclesfield Hunt" and there is a Maxfield Road in Macclesfield. Bearing in mind that Elijah Ridings was from Failsworth nr Manchester, it seems logical that he should use a local hunt song/tune. Further investigation is under way to see if the Macclesfield Hunt tune fits the words to "The Crown and the People's League" as written above.

There is also a Maxfield in Oxfordshire as well the Avon one that Jack mentions above.

Cheers
Mark