As UK sets poll date, a voter’s dilemma: Vote on party, or vote on Brexit?

As secretary of the rugby club, a social pillar of his village, Brian Newman has heard it all. Leave versus Remain. In versus out. Three years on, Brexit is still a topic of conversation at the clubhouse bar, an argument and a riddle that never quite ends.

On this frosty Sunday morning, however, the minds of the 50 men packed into an upstairs room are focused on Wales playing South Africa in the Rugby World Cup. Some wear the maroon shirt of Penygraig RFC, one of the oldest rugby clubs in Wales, tucked into a coal-rich valley. Broomsticks and cobwebs from the previous night’s Halloween party hang on the walls.

Like many in the United Kingdom, voters here are perplexed by Britain’s protracted departure from the European Union, which extended Monday an Oct. 31 deadline after Prime Minister Boris Johnson failed to rush legislation through Parliament. This district voted 60% for Leave in the 2016 referendum, and many of its residents have grown frustrated with the delays – the latest until Jan. 31, more than three years after 17.4 million voted to leave the EU in a referendum.

Mr. Newman is among those who voted Leave. He’s grown sick of delays and excuses from politicians. He compares the referendum mandate to a rugby coach’s instructions to his team on game day. “There’s no wiggle room. We have to leave,” he says.

But the Rhondda Valley, where Penygraig lies, bears no love for Mr. Johnson or his Conservative Party. In this district, an election has long foretold a single conclusion. Locals joke that you could pin a red rosette on a sheep – Wales has many – and win it for Labour, the center-left party that grew out of the union movement that organized the miners in the collieries which defined and disfigured these valleys. Thus the district’s tilt for Leave in 2016, a campaign led by Mr. Johnson and other anti-EU Conservatives, was a shock comparable to Donald Trump’s electoral success among Democratic voters in the U.S. Midwest.

The loyalties of Leavers in Labour, which has struggled in opposition to straddle both sides of Brexit, are now set to be tested again in scores of districts. Mr. Johnson’s Conservative Party won approval Tuesday in Parliament for a poll on Dec. 12 after opposition lawmakers switched sides following a failed election motion a day earlier.

When voters go to the polls, which political loyalty will shine brightest: Brexit or party? It’s a question on which Britain’s political equilibrium could turn, with lasting consequences.

What will voters be voting on?

Labour has dominated Wales for a century, underpinned by seats like the Rhondda Valley, a bastion of working-class leftism. “They have been very predictable. But they also voted for Leave,” says Roger Awan-Scully, a politics professor at the University of Cardiff.

Fewer British voters align today with a political party. In a 2018 poll, fewer than 1 in 10 said they identified with one of the parties. But 44% identified as either Leave or Remain, an indication of how strong feelings have been running over Brexit.

That complicates the pitch of Labour politicians like Chris Bryant, the member of Parliament for Rhondda and a strong Remain supporter. With Mr. Bryant winning 64% of the vote in 2017, nobody is predicting his upset. But for Labour MPs in competitive seats in Wales and other Leave-voting regions, the risk of losing loyalists over Brexit is palpable.

“Labour identification is not what it was in many parts of the U.K. and particularly in post-industrial communities,” says Dr. Awan-Scully.

Mr. Newman, who works in human resources, says he no longer trusts the delivery of Brexit to Labour, the party that he’s voted for all his life. Unlike other disgruntled Leave voters here, he isn’t just threatening to stay home on election day. He wants to send a message: Brexit first.

“I will vote Tory. One hundred percent. Boris is the only person who will get it done,” he says.

By any measure, Rhondda is stony ground for the Conservative, or Tory, party. In 2017 it polled the lowest number of votes – 3,333 – of any constituency on mainland Britain; Plaid Cymru, the Welsh nationalist party, got twice as many votes and finished second.

To win a majority in Parliament, Mr. Johnson needs to pick up seats in Leave-voting regions in England and Wales. But that may be harder than it looks, given the electoral geography, says Joe Twyman, director and co-founder of Deltapoll, a social research company.

Of 50 seats where more than two-thirds voted to Leave, 24 are already held by Conservatives. The rest are Labour seats, half of which could be in play, says Mr. Twyman. But the others are in regions where the Conservatives have rarely won and Mr. Johnson is unpopular. “Winning any of those is going to be a big stretch,” he says.

For pollsters, the biggest uncertainty is what will voters be voting on: Brexit or domestic policy? In 2017, Theresa May, Mr. Johnson’s predecessor, called a snap election ahead of Brexit negotiations with the EU, seeking a larger majority in Parliament. But what was expected to be an election about Brexit ended up being about anything but, and Ms. May’s wooden style and unpopular manifesto fueled an unanticipated Labour resurgence that in turn led to a hung Parliament.

“People snapped back into their party identifications once that was the situation they were in,” says Mr. Twyman. “The same may happen this time around.”

David Lammy, a Labour MP in London, says that all prime ministers call elections on the belief that they can define campaign themes. “This will begin as a Brexit election. But it will not end a Brexit election. It never goes that way,” he told the Foreign Press Association in London.

“Nobody listens to us”

Brexit has proven as divisive in Rhondda as elsewhere. Jack Dando says his extended family are at it most days, sniping across the kitchen table. “My grandparents are out, out, out. My sister is in, in, in,” he says.

Mr. Dando, a salesman for a construction company, says he voted Remain and points to EU grants that paid for regeneration projects in Rhondda, which is in one of Europe’s poorest regions. Still, he’s not impressed by opposition MPs in Parliament who are throwing sand into the works. “They’re like a bunch of kids,” he says. “Get it sorted.”

He votes Plaid Cymru and feels no allegiance to Labour, unlike his grandparents and other village elders who worked for the coal mines until the 1980s when Conservative Prime Minister Margaret Thatcher faced down a national strike, earning her lasting enmity in these valleys.

“I may be a multimillionaire. I still would never vote Conservative,” says Terry Morris, a self-identified socialist and pro-European. Mr. Morris, a former union activist who works as a gas fitter, voted Remain. But he understands why many of his fellow club members identify as Leavers after decades of economic and social decay. The club’s rugby pitch across the street is built on one of the 58 pits that used to provide steady jobs and community pride up and down the valley, all closed now.

“Nobody listens to us. Nobody is fighting our cause,” he says.

In the 1960s, nearly half of voters identified with a political party. That identification, which mapped onto British social class, has fallen away, says Julian McCrae, managing director of Engage Britain, a civil society organization. “It’s a cohort effect. Younger groups are less likely to see the political world through that lens.”

Since 2016, tribal party loyalty has given way to Brexit identities that have been blamed for polarizing the public and straining democratic institutions. Mr. McCrae agrees that Britain is divided on Brexit. But he argues that on key issues like tax policy and public spending there is more that divides than unites either the Leave camp or the Remain camp – those fragile bonds suggesting to him that it may not harden into U.S.-style polarization that scorches common ground.

“These Brexit identities are new and not ideological and issues-based,” he says.

Mr. Newman says he’s fed up with Brexit and the arguments it generates. Still, he finds himself listening to an hour of news in the car on his daily commute, catching up on the political push and pull that reminds him of a rugby scrum. And he may be an outlier in switching sides here, given the residual strength of antipathy toward the Conservatives.

“Labour has been dominant here for a century and that doesn’t happen here by accident. No one should underestimate the resilience of the Welsh Labour Party,” says Mr. Awan-Scully.

Upstairs in the clubhouse, the Welsh national team goes down fighting to South Africa, ending their hopes of making next week’s final in which England will play. Fans groan at the final whistle, then stream out into dazzling morning sunshine.