There's Brixham net co which is for the fishing fleet, a chandler near the marina office which stocks most things you may need. Then there's Woods at Crediton which has huge amounts of ex RN surplus at good prices.
Not sure what you mean by "decent" or "old fashioned" but I went to a good one in Kingswear (opposite Dartmouth) which is only a few miles from Brixham.
Slightly further afield at Exeter is John Bridger Marine, nice people and willing to get most things. By the side of the old canal basin quite near the city centre if your interested.