JUDY WOODRUFF: But, first: There are reports that the United Kingdom's process to begin leaving the European Union may not begin until later next year, delaying the U.K.'s so-called Brexit.

The June vote to leave may have surprised many there, but it came as welcome news to the island nation's fishermen. They have long complained about European Union rules, and now they're hoping Brexit will help them revitalize a fishing industry they say was damaged by E.U. policy.

From Southwest England, special correspondent Jennifer Glasse reports.

JENNIFER GLASSE: Fishermen have brought their catches into Brixham Harbor since the Middle Ages, when it was the biggest fishing port in Southwest England.

The harbor and the fleet have changed over the centuries. And skipper Mike Sharp hopes there are more changes to come. That's why he voted for the U.K. to leave Europe.

MIKE SHARP, Skipper, "Emilia Jane": We have all the Dutch, and the French, and the Belgian fishermen, and mainly the Spanish as well coming to land to take our fish out of our waters, which we want to — you know, I think we still can let them come in, but we can decide how many comes in.

JENNIFER GLASSE: European Union-mandated quotas stipulate what kind and how many fish the trawlers can bring in. Sharp and other fishermen here claim the quotas favor boats from continental Europe. E.U. rules also limited the size of fishing fleets.

MIKE SHARP: When I started fishing 30 years ago, there was 60 beam trawlers, and now there's 17. So, I would like to see it built back up.

JENNIFER GLASSE: A larger fleet could mean hundreds more jobs for deck hands, engineers, welders and, onshore, processing, buying and selling fish.

Brixham Fish Market is already the largest on England's South Coast, handling about $35 million of annual trade. This market itself was modernized in part with E.U. funds.

PAUL MORTIMER, Brixham Trawler Agents: A lot of the fish we sell in England, we sell from this market here actually goes abroad. I think just because we're out of the E.U., I don't think they're going to stop buying our fish. They're still going to want our fish.

JENNIFER GLASSE: Fish buyer Steve Farrar says his children voted to stay in Europe because they want to be able to study and work there.

STEVE FARRAR, Fish Buyer: Oh, I don't want them that badly.

JENNIFER GLASSE: He voted to leave because he says it was a question of democracy vs. control from Europe.

STEVE FARRAR: I felt very much that if I couldn't vote somebody, a politician, in or out, I didn't want them making decisions over my life or my children's lives or my grandchildren's lives. And that was the fundamental issue, really.

JENNIFER GLASSE: Robert Simonetti exports fish and serves it at a local restaurant, including, what else, fish and chips. He doesn't think his out vote to leave will change much for his businesses.

ROBERT SIMONETTI, Restauranteur: For me, it was all the immigration thing. I think that's a big issue for everybody.

You know, we want control about who comes into our country, really, the people we don't want, the criminals. If you're coming here to work and you're going to be part of the community, we don't care what color you are, whether you're white, black or yellow.

JENNIFER GLASSE: Waitress Wendy Lanyon says any sacrifices made to leave Europe will be worth it.

WENDY LANYON, Waitress: I do believe we're going to — it's going to be hard for us as a country, but nothing like what they made out it was going to be. But we have survived before without being in the European Union. And we will survive again. I'm sure we will.

JENNIFER GLASSE: Despite the anti-Europe sentiment here, this harbor town has deep historical ties with the continent.

Dutch Prince William of Orange landed here on the 5th of November, 1688, and he became the king of England, ruling alongside Queen Mary. Napoleon Bonaparte never actually set foot on land, but his ship was just offshore before he was sent into exile.

Over tea, local historian Edgar Lawrence says it's no surprise Britons voted to leave.

EDGAR LAWRENCE, Historian: I'm old enough to have voted for the common market, but what we got wasn't anything like what we had been told it was going to be. And it's just got worse and worse.

JENNIFER GLASSE: And what do you think Brexit will do for Brixham and Devon and Cornwall?

EDGAR LAWRENCE: Depends very much on the politicians. We know what we want it to do. Will they agree to everything we want, which Europe doesn't seem to want us to have?

JENNIFER GLASSE: The picturesque beaches of Devon and Cornwall counties attract tourists that bring in revenue, but not enough to keep the local economies afloat.

This area once produced tin and copper and china clay, but all you can see of the mines now are now abandoned shells. After the mines closed, there was a steady decline in manufacturing and other industries, leaving this one of the poorest areas in Europe.

Cornwall alone has received hundreds of millions of dollars in European aid, support that's now at risk.

The E.U. had pledged $650 million through 20 to Cornwall to continue to support new businesses, build infrastructure and complete high-speed Internet access to the region.

The head of the local county commission is trying to ensure the money keeps flowing, whether from Europe or the U.K. government.

JOHN POLLARD, Leader, Cornwall Council: I don't think the economic argument played a very big part in the decision. It was more on fear and a dislike of Brussels. People like to blame somebody for the ills of the country, and Brussels was getting the blame. So, it wasn't, in that sense, economically logical. It was very much a reaction vote.

JENNIFER GLASSE: One of Cornwall's poorest areas is Redruth. This food bank gives out free provisions to the needy.

Vikki Rostron and her partner are both unemployed and have six children between them. She has no interest in politics and didn't vote.

VIKKI ROSTRON, Redruth, Cornwall Resident: I didn't know enough about it to think about it, to be honest. It's not — it wasn't something I wanted to do, you know?

JENNIFER GLASSE: The food bank's founder says the Brexit vote won't hurt Cornwall because European money has not produced the right kind of jobs since the local economy has evolved.

DONOVAN GARDNER, Food Bank Founder: Those jobs are not here anymore. And that — and they're still not here. Whether it's European money or British government money, those cyber-jobs are not here in Cornwall. And that's what we struggle with.

JENNIFER GLASSE: Some in Cornwall want the government to bring back heavy industry, not a viable prospect. And European funds have been spent to create 21st century solutions to Cornwall's limitations.

JOHN POLLARD: A lot of that money is not visible, so it doesn't build a school or a sports center. It builds a road, or it builds a business park, or it helps to develop a digital industry. And people, the man in the street doesn't — they don't see that.

JENNIFER GLASSE: Back in Brixham, the fishermen head out to sea. They say they have done their part, persuading the country to vote to get out of Europe. Now it's up to the politicians.

Negotiations are expected to take two years or many more. The fishermen of Brixham hope officials in London and Brussels won't leave them high and dry.

Reporting for the "PBS NewsHour," I'm Jennifer Glasse in Brixham, England.