Don’t bet on a British exit from the European Union. Bet on David Cameron, Britain’s prime minister, who is turning a weak hand at home into a strong suit against the EU.

Extracting strength from weakness, Mr. Cameron has been warning the Continentals that his country might vote for “Brexit” in the June referendum if the EU doesn’t deliver on his demands: It’s up to you to save the Union. Add the unspoken threat of Mr. Cameron’s own exit.

It’s blackmail with the gun pointed at oneself, and the gambit is working very nicely. Last week, Donald Tusk, president of the European Council, dispatched a letter laying out a convoluted offer of surrender. It comes in four points:

• Sovereignty. An “ever closer union” doesn’t “compel all Member States to aim for a common destination.” That’s eurospeak for the “opt-out” London has been demanding since the days of Margaret Thatcher. Britain doesn’t gain a full-blown veto, but it does get a “red card” by which 55% of national parliaments can block further centralization. That won’t be hard to do, given the populist agitation against Brussels rising across the EU.

• Welfare Benefits. EU citizens flocking to the greener pastures of England won’t get in-work benefits such as wage subsidies. Nor will they get unemployment pay for the first three months. If the flow continues, Britain could apply an “emergency brake.”

• Euro vs. Pound. Deepening the monetary union “will be voluntary for Member States whose currency is not the euro,” Mr. Tusk soothes. So stop fretting, the pound is yours, and the Bank of England is boss.

• Regulations. The letter pledges less red tape by “lowering administrative burdens.” London needn’t hold its breath. The mantra has been around for decades. But it’s a victory on principles.

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Naturally, Britons clamoring for Brexit are fuming. The Express reports “growing anger.” The Telegraph mocks Mr. Cameron’s “dance of the seven veils.” Nigel Farage, leader of the EU-bashing U.K. Independence Party, slams the offer as “pathetic.” Yet the Guardian has it right this time, observing that “the PM has wrung real concessions from Brussels.”

The Continentals have indeed yielded on the basics. The rest is just haggling about the devilish details between now and June.

If Mr. Cameron is playing a reckless game, he does so at the home table only. Public opinion, whipped up by the eurosceptic Tories and UKIP members in cahoots with the tabloids, has been tilting toward Brexit. Some polls have the two sides running neck and neck. But the more they rant, the more they strengthen Mr. Cameron’s hand as he takes on France, Germany and Italy, the “Big Three.” Mr. Cameron knows this, and so do the Continentals.

All eyes are of course on Germany’s Chancellor Angela Merkel. She praises Britain as a “natural ally” in the battle for “more EU competitiveness,” where the booming U.K. shines forth while France and Italy groan under double-digit unemployment. But economics is but one reason that Mrs. Merkel insists on the U.K. “remaining a member of the EU.”

Britain embodies cultural affinity. It’s a 1,000-year-old liberal state with a global outlook that favors openness and free trade. In a crunch, London will use force abroad, which the chancellor’s own electorate is loath to do. And Britain makes for a counterweight against French Continentalism. Count on Mrs. Merkel to pull the right strings.

Paris is all bluster when it comes to “Perfidious Albion” as saboteur of “ever deeper union.” But in truth, the French also want Britain as counterweight—as reinsurance against Europe’s No. 1, Germany.

Europe won’t be better off without Britain. But neither would the U.K. without the EU. Isolation wouldn’t be splendid. Britain would lose leverage in Washington, cede London’s financial primacy to Frankfurt and scare off investors who use the Isles as a springboard into the EU’s markets.

Then there is the sheer illogic of leaving the EU.

The false dream is to pry off Brussels’s heavy hand and to seek happiness in the wider European Economic Area. True, the EEA extends the benefits of the single market beyond the EU’s 28 members to such heavyweights as Iceland, Liechtenstein, Norway and Switzerland. But EEA members are subject to the same regulations as the EU core. The tag-alongs pay into the EU’s coffers, but cannot help write the rules. An exit from the EU would therefore leave Britain with a similar burden, but no say—a net loss.

It shouldn’t exceed Mr. Cameron’s rhetorical savvy to score on this point in the battle for his nation’s hearts and minds. Plus, precisely because he is hounded at home, he brings the greater blackmail potential to Brussels the table: If I lose, the yahoos win, sending the Union into tailspin.

Mrs. Thatcher played the same winning game in 1984 when she bellowed: “We want our money back!” Once more, the duel isn’t about the principle, but the price, of Britain’s membership in the EU. Trust Europe to pay more. And trust Mr. Cameron to gild the goodies he brings back as a full-scale victory. The odds are on his side.

Mr. Joffe is the editor of Die Zeit in Hamburg and a fellow of the Institute for International Studies and the Hoover Institution, both at Stanford.

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