I am fairly close to you, and I also had real trouble to find someone when I first moved here. I recommend working your way down the list and begging.
I found that the ones from Yeovil and south wouldn't go north of the A303 and the ones from Langport\Shepton etc said I was too far south. It was a few years ago now, so things might have improved!
I can't give you the number of my farrier (that I found through the begging and crying down the phone method), because, first I would be in for a telling off :->, and second because I know he wouldn't come to you as he has moved to Dorset and will only take on new people in that area.
I can recommend J Sommerville. J Hodges, Andy Manners and Ross Courderoy (I think that's how you spell it) in the North Somerset area, don't know if they will travel?
Or failing that what about a barefoot trimmer if it's just a trim? My mate has hers barefoot and swears by hers.