Immigration was at the heart of the campaign in the U.K. to leave the European Union—though it was by no means the only issue—and when the votes were ultimately counted, a comfortable majority, 52 percent to 48 percent, chose to leave the bloc.

“The political message from the referendum is for more control on
immigration,” Will Somerville, the U.K. senior fellow at the Migration Policy Institute, told me. “And that's a very clear message.” But what’s not clear yet is whether and how that message will actually result in significant reductions to immigration into the U.K.

Indeed, the message had already been clear for a long time. As Reihan Salam pointed out in Slate last week, starting in 1997, Tony Blair, the former British prime minister, presided over a transformation of immigration into the U.K.

“Over the following years, roughly twice as many immigrants arrived in the United Kingdom as had arrived in the previous half-century,” Salam wrote. “Many who arrived during that earlier era hailed from the Caribbean and South Asia, and by the early 1990s, 7 percent of England and Wales’ population belonged to ethnic minorities. By now, that share has grown to over 14 percent.”

That transformation, coupled with unfettered immigration from EU member states, evoked responses ranging in intensity from mild anxiety and desire for controlled immigration to outright xenophobia and insistence that all immigration stop (though many people also welcomed the newcomers). Starting in 2010, David Cameron, now the outgoing British prime minister, tried to apply stricter controls to non-EU immigration into the U.K. But the results weren’t what had been expected: The government’s rules did not apply to family unifications, international students, and high-skilled workers who came to the U.K. with a job offer. Last year, the number of immigrants who came into the U.K. to stay for a year or more was 300,000, roughly split between EU and non-EU citizens.

And since the U.K. controlled its own policies on immigration from outside of the EU even prior to the Brexit vote, the next British leader’s task in the wake of the referendum results will be proving he or she can reduce immigration to the U.K. from within the bloc. But what will that cost the country? “In my view, the answer is: [The U.K.] can [control immigration], but if it does so it will pay a price during negotiations on a new trade deal with the European Union,” Somerville said.

Indeed, the nature of the U.K.’s future relationship with the EU is now the subject of tense discussions not only in London, but also in Brussels. Boris Johnson, the former London mayor who was the head of the “leave” campaign and is seen by many as Cameron’s likely successor as prime minister, wrote this week in The Telegraph that he did not think the “Brexit” vote was about immigration from within the EU at all.

“EU citizens living in this country will have their rights fully protected, and the same goes for British citizens living in the EU,” Johnson wrote in his column. “British people will still be able to go and work in the EU; to live; to travel; to study; to buy homes and to settle down. … [T]here will continue to be free trade, and access to the single market.”

Johnson, in addition to other British politicians (and even President Obama), envisions a relationship with the EU that is akin to Norway’s. Norway is not an EU member, but it’s part of the European Economic Area, which gives it access to the single market, in exchange for which it, among other things, allows the freedom of movement within its borders for EU citizens—that same freedom of movement that many British voters want to limit. Indeed, while Johnson in his column said that British people will be able live and work in the EU, he pointedly did not mention whether the citizens of EU countries will be accorded that reciprocal right.

“By leaving, my view and I believe that of most observers, is that if we were to negotiate full access to the single market with no tariffs on trade, we would have to accept free movement of labor,” Somerville told me. “Now that seems to be incompatible with what this vote was about. So if we do control European migration, it seems to me inevitable that there will be some limits on our access to the single market: whether those limits are tariffs or whether those limits are variable tariffs, I think that’s all to be negotiated.”

As if underscoring that message, Donald Tusk, the president of the European Council, said Wednesday: “There will be no single market a la carte.” Meaning the U.K. cannot pick and choose those aspects of the single market it likes, such as tariff-free trade, and reject those it doesn’t—like freedom of movement.

But even before they get to that sticky issue of freedom of movement, U.K. and EU negotiators will have to contend with the approximately 3 million EU nationals who now live in Britain and the about 1.4 million Britons who live in Europe. It is seen as highly unlikely they will be expelled, or repatriated en masse, and, in fact, in a post-Brexit world many could be accorded the rights and entitlements they already enjoy. But, says Somerville, “there will be a countervailing force, which is that this will be an issue on the table during negotiations on exit and so I don’t think we’re going to get clarity that quickly.”

One of the few things on which there is clarity is that when the U.K. invokes Article 50 of the Treaty of Lisbon—the starting gun, as it were, on leaving the bloc—EU immigration to the U.K. will likely slow, even if it doesn’t stop. The U.K.’s current points-based system that applies to non-EU nationals could be expanded to include EU nationals, as well. That system tends to favor a particular type of immigrant.

“I think you would see a shift toward more qualifications, higher-income, higher-skilled workers,” Somerville said. “And you’d see an overall reduction in the numbers coming from Europe,” especially from places such as Poland and Romania, where workers tend to be younger, less experienced, possessed of fewer qualifications, and, consequently, earn less. This, Somerville warns, will result in an increase in other channels of migration, including family reunions and illegal immigration, to get around the system.

But before any of this can happen, the U.K. must invoke Article 50, which Cameron says is the next prime minister’s job, and Johnson says he’s in no hurry to invoke. And the turmoil in both of the U.K.’s major parties may further complicate the complex process that is destined to follow.

“There has been a clear division and polarization in the electorate for some time,” Somerville said. “And this [the referendum] has shown it very sharply. It’ll become very important for the Labour Party, as well as the Conservative Party, how some of the next phase unravels.”