Barely hours after British voters had decided to leave the European Union, reports started appearing about some Brexit voters suffering buyer’s remorse. Fair enough, and one doubts their numbers would have been great enough to shift the result. The more interesting question in the weeks ahead is whether Leave campaigners might start suffering a rarer form of winner’s remorse. The Leave result is a poisoned chalice for the politicians who campaigned for it. To them falls the task of presiding over an economically tumultuous period. Sooner or later they will also have to explain to voters that Britain’s economic ills did not spring from its membership in the European Union. The economic unease underlying so many votes for Leave is real, even if the EU’s blame for many of the problems was exaggerated. The Conservative Party under Prime Minister David Cameron delivered annual growth between 2% and 3% for most of the past six years, and the unemployment rate of 5.4% is at an impressive low even as the percentage of Brits in the labor force is at unusual highs. But that growth has not been evenly distributed across the country. London and some cities have boomed on the strength of financial services, information technology, artistic and design fields and the like. Such firms are great beneficiaries of EU membership that allowed Britain to position itself as a services hub for Europe. No wonder greater London was the only region in England to vote decisively to Remain. (Scotland and Northern Ireland backed Remain chiefly for cultural reasons.) It has been a very different picture elsewhere. The large-scale manufacturing that provided prosperity to so many British regions has been in steady decline for more than 30 years. In a telling coincidence, the two biggest business stories in Britain in the months before the referendum were the collapse of a venerable department-store chain and the threatened closure of a Welsh steel mill, done in by the growth of internet commerce and global competition, respectively. As in other developed countries, no one has figured out how to replace those jobs with work of the same quality and stability. The EU provided a convenient foil to politicians of all stripes in this regard. “The EU” prevented Britain from imposing punitive tariffs on Chinese steel to save British jobs. “The EU” flooded Britain with immigrants who undercut local workers on wages and drove up housing prices. “The EU” imposed burdensome and costly regulations on struggling small businesses. The bulk of industrial-heartland England went for Leave, as did industrial Wales. This was a deceptive argument, however, because much more of the blame for Britain’s problems resides at home. Britain, not the EU, encouraged lavish green subsidies and renewable-power mandates that have driven out manufacturers with high energy costs. Britain, not the EU, imposed increases in consumption taxes—to 20% from 17.5%—to pay for unsustainable entitlement spending by extracting more money from a struggling middle class. Britain, not the EU, implemented the monetary policies and building restrictions that combined to inflate housing prices beyond the reach of a growing number of young people. The Leave campaign now must explain this, and the need to reform these and so many other measures, to voters who have been led to believe that a clean break from the European Union would be enough. The difficulty of the task will be compounded by its urgency, as the tumult arising from Brexit places the economy under ever greater strain. It can be done, but not easily. British voters have embraced economic reform before, most recently under Margaret Thatcher in the 1980s. Under Mr. Cameron they accepted significant welfare overhauls and some spending reductions. Leave campaigners, or some of them anyway, have laid the groundwork by arguing that Brexit will free Britain to pursue a far more liberal economic order. But did Leave voters really grasp the message that they should leave the EU so that they can implement difficult reforms? Note that Britain was nowhere near exhausting the list of reforms it could implement from within the EU. Instead, the country recently rejected the most modest of tweaks to its disability-benefit system; an attempt to flatten the personal-income tax by reforming low-income credits; and even an effort to liberalize Sunday trading hours so grocery stores can stay open longer on weekends. None of these measures ran afoul of EU rules and none would have required permission from Brussels. Worse for Leave leaders, a press corps previously prepared to defer to Brexiters as one of the two evenly matched sides in a political campaign will now treat them as normal politicians facing tough policy questions. Their new authority gives them nowhere to hide. One sign of trouble: The generally pro-Brexit Daily Telegraph newspaper on Friday featured an article on its website “fact-checking” many claims made by both sides during the campaign. The most generous thing it said about the veracity of Leave claims, such as the negative impact of immigration on Britain, was “hard to say.” Others, such as the argument that a liberal Britain is frequently overruled by European protectionists in Brussels, got an outright “wrong.” The euroskeptic-skeptics are coming. Another: Local governments in areas that voted to Leave, such as Cornwall, already are asking when they can expect checks from London to make up for the EU subsidies for things like rural broadband internet they’ll lose. In this most unpredictable of years everyone should be getting out of the “never” business. Perhaps Leave will be able to govern a deeply divided electorate that has narrowly made an epochal change that is having dramatic and negative short-term economic consequences. And perhaps Leave will persuade those voters to accept the challenging reforms the more honest Leave campaigners have admitted all along are necessary. But perhaps there’s a reason Leave’s most prominent Tory backers, Boris Johnson and Michael Gove, looked like they were attending a funeral at their victory press conference Friday morning. Perhaps one of the more dangerous things in politics is to get exactly what you want.