NEWLYN, England—Nothing drives fishermen here crazier than having to comply with European Union quotas by dumping perfectly good fish back into the sea while other Europeans working nearby keep their catches.

“Quite often, we’re working on our grounds, surrounded by foreign vessels who have got more right to fish than we have in our waters,” said David Stevens, a 43-year-old fisherman in Newlyn, the largest port in England by weight of fish sold. He blames the EU’s quota rules for causing the industry to flounder. “We just...