Brexit supporters participate in the "March to Leave" on March 29, 2019, the date Brexit was supposed to happen.Matt Dunham / AP

LONDON—Brexit is an all-consuming maelstrom of political dysfunction, one that has compelled Britain’s eyes inward. Yet amid the chaos, Prime Minister Theresa May has been steadfast in her determination that the country’s international role should not succumb to the same myopic fate as its departure from the European Union has.

In the febrile early months following the June 2016 referendum when Britain voted to leave the EU, its allies were fearful that the vote would see the country’s drawbridges snapping upward. Sensing the urgent need for optimism, May and her then–foreign secretary (and now possible successor), Boris Johnson, gave bold speeches, setting out ambitions for what they called a “truly global Britain.” Conjuring an image of a triumphant, swashbuckling nation retaking its rightful place on the world stage, a global Britain embodies the promise of a Brexit dividend, one in which the country is no longer hemmed in by what Brexiteers see as a European cage.

Almost three years on—through failed parliamentary votes, cabinet resignations, and May’s announcement that she will step down as prime minister—this mantra of internationalism remains one of the few legacies of May’s premiership. So far, however, a global Britain has been nothing more than a hollow promise.

With British diplomats struggling to convince their international peers of the phrase’s fundamental purpose and meaning, a cross-party group of lawmakers leading the parliamentary Foreign Affairs Select Committee warned last year that “Global Britain” had only succeeded thus far as “a superficial rebranding exercise.”

At the heart of the global Britain promise is a great paradox: Those who are most naturally inclined to support such an idea—young, university-educated, well-traveled Britons—fundamentally resent the notion that any project forged on the back of Brexit could be truly internationalist.

Foreign policy has often served only as a sideshow to British domestic politics. However, with Brexit sparking complex new conversations about trade, diplomacy, and defense policy—as well as more elemental questions about Britain’s role in the world—foreign affairs may well become one of the most active battlegrounds of Britain’s deepening social fault lines.

And with about a dozen contenders lining up to replace May as Britain’s prime minister, the future of the ”global Britain” catchphrase and the strategy it was intended to inspire will become central to the Conservative Party’s, and the country’s, future. False silos that have long separated domestic and foreign policy will have to come down.

“Foreign policy isn’t about foreigners,” Tom Tugendhat, a Conservative member of Parliament and the chair of the Foreign Affairs Select Committee, told me. “It’s about us, and how we shape the world around us in the interest of our people, our friends and partners.”

It won’t be easy: New research I have conducted with the British Foreign Policy Group, an educational think tank, and the pollster BMG makes clear that Britain is phenomenally divided on the country’s international identity, spearheaded by a government unable to make the trade-offs necessary to truly achieve the idea of a global Britain. The notion that citizens will instinctively support the costs necessary to become a more prominent military, diplomatic, and trading power does not stand.

Political momentum is instead building behind those who see more downsides than upsides in our changing world, and for whom liberalism and internationalism inspire suspicion, mistrust, or even fear. These Britons generally have lived less mobile lives, hold identities more closely rooted in their communities, and are less bothered by events outside the confines of the nation. For example, just 6 percent of those who traveled abroad frequently last year consider immigration to be an important issue, compared with 44 percent of those who didn’t leave Britain. Among those who never stray abroad, there is, to be sure, a significant degree of distinction between people whose socioeconomic circumstances have hampered their access to international opportunities and the older, wealthier Britons who have chosen to prioritize an exclusive national identity.

May herself supported remaining in the EU ahead of the 2016 referendum. But after the vote, while many of her colleagues in the Conservative Party espoused a so-called Liberal Leave argument—that Brexit would allow Britain to secure new free trade deals and to better work with fast-growing developing countries—she recognized the role that concerns about the economic and social consequences of globalization had played during the referendum. At the first Conservative Party conference following the vote, she spoke to the growing reticence toward internationalism and the clamor for a strong expression of national pride, telling the audience, “If you believe you are a citizen of the world, you are a citizen of nowhere.”

This extraordinary moment broke with 20 years of political consensus behind a form of loose cosmopolitanism, beginning with Tony Blair’s election victory in 1997, signifying the radical early ambitions of May’s premiership. It also pitted her government’s two core messages against each other—at once pushing for a global Britain while denouncing globalism. Ultimately, her efforts to promote a global Britain without the support of global citizens were always doomed to fail.

In a divided Brexit Britain, only one issue provides space for common ground: trade. Those who voted to leave the EU and those who cast ballots to remain differ on many issues—only a quarter of Leave voters support increases to Britain’s overseas spending, and Remain supporters are twice as likely to care about climate change and global conflicts—but all agree that trade should be at the heart of the country’s global priorities.

Although Matthew Elliott, who led the Vote Leave campaign, recognizes that the “liberal, internationalist, free-trading” argument for Brexit was not the primary driving force for core Leave voters, he told me he was certain that it was decisive in persuading swing voters. In this way, the Leave campaign was incredibly effective at mustering diverse constituencies to support the vision of a sovereign, global Britain, unshackled from the EU.

Nonetheless, there is little appetite to stomach the compromises of free trade: Only 26 percent of Leave voters we surveyed would be willing to accept any increases in immigration from, for example, India, one of Britain’s priority markets—even if they were crucial to securing a free-trade agreement.

It can be difficult to reconcile the pulsating tribalism of post-referendum Britain with the immense popularity of the flagrant internationalism promoted by the successive Blair governments. At the 2005 Labour Party Conference in Brighton, the then–prime minister forcefully rebuked the growing disquiet around globalization, announcing, “You might as well debate whether autumn should follow summer”.

Blair’s political fortunes were not evergreen, though. His decisions on economic policy, immigration, and the Iraq War would crucially challenge the public’s trust in an increasingly connected world order and the institutions that seek to uphold it. As Britons cast ballots more than a decade later in the EU referendum, voters had begun to reject the sense of inevitability they had been sold around the nation’s trajectory. Indeed, by 2016, Blair would launch his own policy institute in London, its mission—“Making globalisation work for the many”—hinting at a degree of regret.

Westminster will undoubtedly continue to debate Blair’s legacy for many years to come. It is clear, however, that no other leader in this political generation is likely to inherit the fortuitous climate for internationalism that he enjoyed.

With the clock ticking on May’s premiership, the paradox of a global Britain she unwittingly exposed will need to be reconciled by her successor. The candidates jostling to replace her as the Conservative Party leader and, by extension, prime minister, appear committed to championing a global Britain, but have not yet articulated any means of persuading the large swaths of the country skeptical of internationalism to fall in line.

If her successor calls for a general election and the opposition Labour Party comes to power, it will face its own reckoning around the discord between its membership’s broad support for international institutions and its leadership’s radical positions on unilateral nuclear disarmament, NATO, and the military.

For now, however, the challenge falls to the party that has made itself the party of Brexit and a global Britain, without delivering either.

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