This newfound popularity is due in part to Cameron’s new, gentler political lexicon. Back in 2002, in a much-cited moment of political honesty, Theresa May, a former party chairman and a leading Tory M.P., shocked her audience at a party conference by asserting that the Conservatives were seen as “the nasty party,” a reputation Cameron inherited with the leadership three years later. But gone are the days when the party appeared to stand for red-blooded individualism and unconstrained wealth creation. It is now the Conservatives, not Labour, who complain of soulless materialism among the country’s rulers. In addition to traditional party themes, such as rolling back the power of the state, Cameron’s speeches are peppered with references to “social justice” and “work-life balance.” While campaigning in the Crewe by-election, Conservative Party candidate Edward Timpson carried his 2-year-old daughter on his back.

This modernization strategy has also played on environmental concerns that have helped align the Conservatives with the young, a group long seen as leery of the party. The party’s old flaming-torch emblem is gone, replaced by a fuzzy blue and green image of a tree in full leaf. Cameron has been photographed on a sleigh in the Arctic researching the impact of climate change. He has bicycled to work (albeit followed by aides in a car carrying his papers), and is about to install a wind turbine at his London home. After three years, Cameron is reaping the rewards of his effort to emphasize a softer Toryism and “decontaminate the brand,” says Elizabeth Truss of the think tank Reform.

He has done so under scrutiny from a skeptical media and critics keen to portray him as a shallow opportunist. Last year he took heavy criticism for heading to Rwanda to visit a school-building project while his own constituency was hit by severe floods. One speech suggesting that out-of-control youths needed understanding as much as punishment prompted a spate of headlines ridiculing what the papers called his “Hug-a-Hoodie” line, a reference to the hooded sweatshirts in vogue with young hooligans.

One persistent charge is that Cameron has failed to spell out specific policies. Party activists point to a heap of papers proposing, for example, that parents should be allowed to establish their own state-funded schools, and introducing elected, rather than appointed, police commissioners. Other ideas, such as a special levy on rich foreigners, who are now exempt from British tax, have been filched by Labour and adopted as its own. But voters would be hard-pressed to list distinctive Conservative policies in critical areas such as reforming the National Health Service or combating crime.

On a tactical level, that could be a smart strategy. Setting out policy too far ahead of a national election could risk alienating wavering voters as well as Tory diehards determined to preserve the values that brought the party success in the ’80s and ’90s. Cameron has already irritated hard-liners by refusing to promise lower taxes—once a defining Conservative policy—in the party’s next election manifesto. There are also disquieting parallels with the rise of Tony Blair and his makeover of the Labour Party in the early ’90s. As with Blair, it’s easy to present the Tory overhaul as the work of a small group of young modernizers out of touch with mainstream opinion.

But the party now seems prepared—or resigned anyway—to back any leader who can promise a return to power, says veteran pollster Bob Worcester. “If he can win, then they will back him,” he says. “Even if some of them are holding their noses.” So far, Cameron’s moves seem to be working. Not long ago, says Anthony Browne of the think tank Policy Exchange, “when any Conservative politician opened his mouth, people just laughed.” But with support for the Tories now at more than 40 percent, no one is laughing anymore.