Thiemo Fetzer, an economics professor at the University of Warwick, has found that a significant number of people voted for Brexit not because they were ideologically opposed to the European Union, but rather because they wanted a way to protest after austerity cuts had left them feeling ignored by the government. Those same voters, he says, are now the most susceptible to doubts about Brexit being the best path forward, suggesting that, for them, pocketbook issues outweigh ideology.

Perhaps reflecting those changing attitudes was well-regarded work by Survation, a research firm, that showed support for leaving had fallen around 10 percentage points in Sunderland since the referendum. This was not a traditional opinion poll, however, but an estimate based on responses from 20,000 people nationwide that were combined with information about the demographics and voting history of local areas.

At Pop Recs, a music shop and cafe near the bus depot, three people who voted to stay in the European Union were debating a second referendum. Barry Cornell, 42, worried another public vote risked reviving the far-right U.K. Independence Party, which played a major role in the Brexit campaign. But the shop’s proprietor, Dave Harper, said he did not much care whom a referendum angered, so long as it reversed Brexit.

Laura Brewis, 37, an arts organizer and fund-raiser sitting beside Mr. Cornell at the counter, lamented that elected leaders had said nothing for years about the European Union funding that came to Sunderland.

Grants from the bloc have contributed to an aquatic center and a university campus, and helped underwrite a business center that assists aspiring software entrepreneurs, though these amenities are not always within reach for residents.

In a square in the city center, a monument features the shipyard workers who once made Sunderland the largest shipbuilding hub in the world. It looks like a local project through and through, except for a small bronze plaque nearby covered in browning grass.

Describing the source of some funding, it features not a Union Jack, but the flag of the European Union.