“Far from Brexit disappearing from the news, it will be back with a vengeance,” says Alex de Ruyter of Birmingham City University’s Center for Brexit Studies.

EU officials warn it may be impossible to conclude a comprehensive agreement by December 2020. The exit deal allows for an extension, but Mr. Johnson has ruled this out. Any extension must be requested by July 1, setting up a crunch point early in Mr. Johnson’s term that could puncture his campaign promise.

Under Mr. Johnson’s deal, the U.K. stays in the bloc until the end of 2020 to allow negotiators to draw up new terms of trade. If no agreement is reached, barriers would go up to EU markets, where nearly half of British exports go.

Brexit finally looks set to roll ahead. Prime Minister Boris Johnson’s newly reelected government has a clear path to a Jan. 31 departure from the European Union. But the heated debate over how the U.K. exits the EU is only the prelude to what could be years of wrangling over trade between the two. Both sides have a strong interest in finding a post-Brexit deal. But clashing political agendas could make the next phase of Brexit just as difficult for the U.K.

When Brexit-weary U.K. voters handed Prime Minister Boris Johnson’s Conservative Party a commanding majority in Parliament Dec. 12, they ended a withering political impasse over leaving the European Union that damaged the U.K.’s economy and its reputation as a stable democracy.

Days later, Parliament began to lay the legal groundwork for an exit on Jan. 31, nearly one year from its original deadline. On Feb. 1, the United Kingdom, which joined in 1973, would be out, finally.

Job done? Not exactly.

The heated debate over how the U.K. exits the EU is only the prelude to what could be years of wrangling over trade between the world’s fifth largest economy and its largest free trading bloc. Both sides have a strong interest in finding a post-Brexit economic equilibrium. But a lack of trust and clashing political agendas could make the next phase of Brexit just as difficult for the U.K. and expose its economy to further damage if talks break down.

Grace period or cliff edge?

Under Mr. Johnson’s exit deal, the U.K. stays in the European bloc until the end of 2020, a grace period to allow negotiators to draw up new terms of trade. If no agreement is reached, the U.K. would be out, and barriers would go up to EU markets, where nearly half of British exports go.

EU officials warn it may be impossible to conclude a comprehensive agreement by December 2020. The exit deal allows for a mutually agreed extension of the grace period for up to two years. But Mr. Johnson has ruled this out.

“In case we cannot conclude an agreement by the end of 2020, we will face again a cliff-edge situation,” Ursula von der Leyen, president of the European Commission, said on Dec. 18.

Analysts say Mr. Johnson may ultimately go for an extension, but that the risk of a “hard Brexit” remains. For some of his allies, breaking with EU rules and regulations would unleash British capitalism in a low-regulation economy, a model known as “Singapore-on-Thames.”

Trade talks are expected to start by March and any extension must be requested by July 1, setting up a crunch point early in Mr. Johnson’s term that could puncture his campaign promise.

“Far from Brexit disappearing from the news, it will be back with a vengeance,” says Alex de Ruyter, director of the Center for Brexit Studies at Birmingham City University.

An extension of talks would require the U.K. to continue paying into the EU budget, an unpalatable prospect for the government. Mr. Johnson led the Brexit campaign in 2016 that claimed falsely that the U.K. paid £350 million a week (about $460 million), money that it could redirect to its national health service. The actual net contribution is £212 million, according to the U.K.’s statistics agency, which would likely be dwarfed by the cumulative effects of slower economic growth outside the EU under a free trade agreement.

Mr. Johnson’s supporters say a bare bones agreement for cross-border trade in goods can be agreed to next year – and that by refusing to extend, the U.K. is forcing both sides to find common ground.

Phil Noble/Reuters British manufacturing, like the production at this Nissan car plant in Sunderland, England, is dependent on “just-in-time” supplies from Europe that will be cut off without a trade deal with the EU.

Such an agreement would not, however, guarantee British companies full access to European markets. And it would exclude most services, which are the U.K.’s largest export to the EU, particularly in banking and insurance. EU regulators insist that non-EU partners must meet their exacting criteria for services if they want trading privileges.

Even if the EU shows flexibility, the 27 member states have their own agendas on thorny issues like fishing rights, state subsidies, and data protection. Any comprehensive trade agreement must be approved by lawmakers in each country.

“There’s no way that the EU could compromise on big policy areas where they want to be leaders and to ensure unity in the EU,” says Sara Hagemann, director of the school for public policy at the London School of Economics (LSE).

What does Boris really want?

Perhaps the biggest unknown is what exactly Mr. Johnson, a political chameleon famous for eschewing policy details, wants from a future economic partnership with the EU.

His exit deal differed from his predecessor Theresa May’s in watering down the U.K.’s commitment to mirror EU standards on labor, environmental protection, and other sectors in return for privileged market access. Mr. Johnson has insisted the U.K. can set its own rules and maintain its trading privileges.

“He would like to have his cake and eat it too, but he’s not going to get it,” says Mr. de Ruyter.

A looser relationship would allow the U.K. more flexibility to negotiate with the United States and other non-EU trading partners. President Donald Trump, a political ally of Mr. Johnson and a fan of Brexit, said he wants an “ambitious” free trade pact with the U.K. Still, economists say any U.S. pact wouldn’t make up for a rupture in ties with Europe, given the relative size of cross-border trade.

Mr. Johnson will face intense pressure from U.K. companies not to scuttle EU trade, particularly in industries anchored in the English equivalent of the Rust Belt.

“It could go either way. Don’t assume we’re going to end up with hardcore Brexit,” says Simon Hix, a professor of political science at LSE.

One reason is political calculus: Mr. Johnson won his majority by peeling away left-leaning voters in the Midlands and North who are more likely to work in manufacturing and food processing. “He has to deliver to those constituencies a Brexit that’s beneficial to them,” says Dr. Hix.

The size of Mr. Johnson’s majority also lessens his dependence on free market Conservatives who lionize a low-regulation economy.

In the West Midlands, up to 50,000 jobs depend on automakers who have warned of the risks that a hard Brexit creates for “just-in-time” manufacturing that relies on a web of parts suppliers outside the U.K., says Mr. de Ruyter. Toyota’s auto plant in Burnaston, for example, only stocks four hours worth of parts for the models it produces and relies on daily deliveries of parts from trucks that arrive from mainland Europe via the Port of Dover.

Even a trade deal that avoids tariffs and quotas on goods from Europe but adds to waiting times at ports is a setback. “I’m not sure that a bare bones deal would be enough for manufacturers,” he says.

Sir Ivan Rogers, the U.K.’s former top diplomat at the EU, has warned of a repeat of last year’s debacle if the U.K. fails to think and act strategically. “I believe the biggest crisis of Brexit to date actually still lies ahead of us in late 2020,” he said in a pre-election speech at the University of Glasgow in Scotland.

Sir Ivan, who resigned in 2017 over the U.K.’s handling of Brexit, said he believed a Johnson victory would play into the hands of EU negotiators who know the prime minister will refuse to extend trade talks. That creates a “huge, open goal opportunity” for the EU to lay out its preconditions for a close relationship and force Mr. Johnson to choose between an unpalatable trade deal and a hard break that could wreck the U.K. economy.

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“We have lived in a European world where more and more of those barriers within Europe have been taken down, and where we have helped reduce the barriers between that European world and more other jurisdictions than has any other trade bloc in the world. All those barriers go up unless and until we agree with others to remove them,” he said.

The EU-U.K. relationship could end up as “thin, sour, and conflictual,” Sir Ivan said. “That is in neither side’s best interest. But it might require real vision from both to avoid it.”