Britain’s chattering classes are calling prime minister David Cameron’s speech last week the most significant of his political career. Indeed, in its clarity and forthrightness, it managed to make the punch-drunk and increasingly cynical bulk of British voters sit up and take notice.

Responding to pressure from all sides—not least from his own party—Cameron made a binding pledge to hold a referendum in the next parliament on whether Britain should remain within the beleaguered European Union. While proclaiming his own belief that Britain should stay in the E.U., Cameron acknowledged the mounting Euro-skepticism in the country. The E.U., many now feel, is no longer the organization Britain joined 40 years ago. Cameron’s proposal is simple: during a second term as prime minister, he would attempt to renegotiate the terms of Britain’s E.U. membership—establishing a looser association, with certain powers repatriated to the British parliament.

If this effort proved successful, Cameron would recommend the new deal to the country and campaign for a “Yes” vote in the referendum. Presumably, if he were unable to secure Britain’s new arrangement with the E.U. he would campaign for a “No” vote. Being a politician first and foremost, though, he left this question hanging.

Cameron’s speech left other contingencies unaddressed, not least of which was that the described course of action would hinge on his winning the 2015 election, a prospect that currently appears remote. Battle-weary Euro-skeptics worry that if he somehow does win, he would dress up a bad deal with the E.U. as a glorious victory on which to campaign for Britain’s continued membership. Such fears are understandable; all too often, British prime ministers have presented mere tinkering and promises of reform as great leaps forward.

Cameron’s tone and language ensured that his speech would go down well with what is now mainstream opinion. Parliament’s anti-E.U. Tories, who otherwise have little time for him, called it the most Euro-skeptic speech ever given by a British leader, one they had waited to hear “for 40 years.” Certainly in its acknowledgment of public frustration, Cameron’s speech was refreshingly populist; voters have grown weary of a political class that seems only to talk to itself. But Cameron’s most striking words went largely overlooked: “There is not, in my view, a single European demos.” He thereby denied, at a stroke, one of the E.U.’s founding assumptions.

A veteran activist of referendum campaigns explained why Cameron’s two-step approach was so well received. People want to give it a fair throw of the dice, he said, and see if we really can work something out. He compared it with a troubled marriage. First you go to counseling to try to work the problems out; only when all else fails do you head for divorce court. But one can’t help reflecting that more often than not, a trip to the marriage-guidance office usually signifies that something basic has already changed forever.

Peter Whittle is founder and director of the New Culture Forum, a columnist for Standpoint, and author of several books, including Look at Me: Celebrating the Self in Modern Britain and Monarchy Matters.