I have listed all those within a reasonable drive.
Bridgwater Farmers Market
2nd Fri of the month, High St.
Glastonbury Country Market
Tuesdays 9.30-12.30 Town Hall
Glastonbury Farmers Market
4th Sat of the month, 9.00-1.00 St.johns car park
Langport Country Market
Fridays 8.30-11.30 Ridgway Hall, Bow St.
Minehead Country Market
Fridays 9.00-11.30 Friends Meeting House
Taunton Country Market
Wed,Thur,fri 8.00-2.00 Sat 8.30-1.00 Bath Place
Taunton Farmers Market
Thur 9.00-3.00 High St.
Wellington Farmers Market
3rd Sat of the month, The Square