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.

Read: The race to replace Theresa May: a cheat sheet

“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.