"imaginary west-of-England country dialect used on stage," by 1925, from mummer + Somerset.
Entries linking to mummerset
mummer n.
"one who performs in a mumming, actor in a dumb show," early 15c., probably a fusion of Old French momeur "mummer" (from Old French momer "mask oneself," from momon "mask") and Middle English mommen "to mutter, be silent," which is the source of mum (interjection). "[S]pecifically, in England, one of a company of persons who go from house to house at Christmas performing a kind of play, the subject being generally St. George and the Dragon, with sundry whimsical adjuncts" [Century Dictionary].
Somerset
9c., Sumor sæton, from Old English sumorsæta, short for *sumorton sæte "the people who live at (or depend upon) Somerton," a settlement attested from 8c. (Sumertone), and meaning "summer settlement." In 12c. it begins to be unmistakably a place-name (Sumersetescir) not a collective name for a people.