British and European officials are increasingly hopeful they can heal some of the divisions over the U.K.’s split from the trading bloc, including a long-running dispute over Northern Ireland, as the war in Ukraine pushes both sides closer and opinion polls suggest British support for Brexit is waning.

U.K. Foreign Secretary James Cleverly and his European Union counterpart, European Commission Vice President Maros Sefcovic, will meet Monday and are expected to signal the start of final negotiations on a compromise agreement over the trading status of Northern Ireland, an issue that has created tensions between both sides and threats of a trade war. 

Resolving the Northern Ireland issue would also help the U.K. government’s standing with the Biden administration, which has repeatedly said it wants the issue resolved without damaging long-term prospects for peace in the often troubled British province. 

The talks mark a realization by both the EU and Britain that there is little to be gained by antagonizing each other and much to be lost by disrupting trade further at a time of economic hardship in Europe caused by the war in Ukraine, high energy prices and inflation, analysts and officials say. Britain’s support for Ukraine during its war with Russia has reminded EU officials that it is an important ally, helping foster renewed trust between the two sides, European officials say. 

The mood about Europe has also changed in the U.K., which has struggled economically since its 2016 vote to leave the EU. Absent growth, U.K. officials are now focused on steering the economy through a likely recession. “A big reason is that the context has changed,” said Jess Sargeant, a researcher at the Institute for Government, a U.K. think tank. “Before it was delivering on Brexit, now it is very much about the economy.”

A YouGov poll in November said support for Brexit had fallen to a record low in the U.K., at 32% in favor.

The years after Britain quit the trade bloc in 2020 have been marked by acrimony and political point-scoring on both sides of the English Channel as Britain tried to forge a new path independent of the trade bloc and EU nations worried it would undercut them by aggressively deregulating its economy. Those fears have subsided, officials say. 

“When we first left the EU, it was raw, and it was visceral, and tempers ran high on both sides of the channel,” said one senior British official. 

As part of its 2019 divorce deal with the trade bloc, Britain agreed to the so-called Northern Ireland Protocol, placing a customs border within its own country to avoid building border infrastructure between Ireland, an EU member, and Northern Ireland, part of the U.K. It did so to avoid inflaming sectarian tensions among the Catholic Irish nationalist community in the province, which has long had tensions with the mostly Protestant unionist communities. 

But customs checks within the U.K.—which take place mostly in Northern Ireland ports—angered unionists in Northern Ireland who felt split off from the rest of the U.K. And ever since the deal, the British government has tried to back out. Eight months ago, Britain was threatening to pass a law that would allow it to unilaterally rewrite parts of its divorce treaty with the EU, in a bid to force the EU to fold. The EU, for its part, threatened to suspend Britain’s trade deal with the EU in retaliation. 

The Biden administration publicly urged the U.K. to find a negotiated solution, fearing a damaging spat between allies as war in Ukraine raged.  

Some officials say a revised deal, that would lessen customs checks, could come together in a matter of weeks, though they warn political hurdles could still emerge and some issues may need to be returned to. Others are eyeing the 25th anniversary of the Good Friday Agreement, which resolved the conflict in Northern Ireland, in April as a deadline.

After the 2016 referendum to quit the EU, the ruling British Conservative party championed actively diverging from the trade bloc in a bid to forge Britain’s own path on the global stage. The government argued that it could create nimbler regulations, control migration and forge closer ties with fast-growing economies.

That vision, which it branded as “Global Britain,” “is dying,” said Bronwen Maddox, the director of Chatham House, a think tank. A major trade deal with the U.S., which was touted as an alternative to Europe, looks unlikely. Since its EU exit, Britain’s economy is 5.5% smaller than it would have been, according to analysis by John Springford, an economist at the Centre for European Reform, a think tank. Illegal migration has spiked and the government needs French cooperation to stop small boats filled with asylum seekers crossing the Channel.

To solve these issues, “all roads lead to Europe,” Ms. Maddox said. This rapprochement began during the short tenure of U.K. Prime Minister Liz Truss after the U.K. markets hit turbulence following an unfunded tax-cutting budget. Her successor, Rishi Sunak, doubled down, promising “respectful, mature relationships” with the bloc.

The U.K. opposition Labour Party has urged Mr. Sunak’s government to strike a deal. “Labour will give the support needed to get a protocol deal through Parliament and work in the national interest to secure peace and prosperity in Northern Ireland,” Labour leader Keir Starmer wrote on Friday. 

Any deal might also face opposition from the Democratic Unionist Party in Northern Ireland, which was angered by the Northern Ireland Protocol and pulled out of a power-sharing agreement among the province’s different factions, shutting down the Northern Ireland assembly. The U.K. government says the assembly must return to ensure peace. 

European diplomats say if the Commission and Ireland find a deal they believe can work with Britain, most other capitals are unlikely to object, although there is some nervousness about the intensity of French concerns about the protection of the bloc’s single market.

In recent days, the EU and the U.K. agreed on the data-sharing systems to give EU authorities assurances that goods meant not to cross into the rest of the EU’s single market stay in the province. 

Perhaps the toughest issue remains governance in Northern Ireland. Britain wants to end the role of the European Court of Justice in interpreting the application of EU law in Northern Ireland, a role that EU officials say is crucial given the province’s de facto place in its single market.

The issue has become a political litmus test for Mr. Sunak’s ability to control Brexit supporters in his Conservative Party who argue that no part of the U.K. should be governed by EU law.  

Nonetheless, people involved in the talks believe a compromise—perhaps through additional layers of consultations and arbitration before the EU court is brought in—is possible if the other issues are resolved.