Churchillian it isn’t. But Cameron has a problem with the past, his party’s and his own. His Tories are on a roll; one poll last week gave them a clear seven-point lead over Labour. But the party is still struggling to recast itself not merely as a natural home for the rich and privileged, but also for more modern voters interested in social conscience as well as tax cuts. To do that, Cameron needs all the street cred that his media spinmeisters can muster. Yet they can’t quite conceal an awkward fact: in an era when class is no longer supposed to matter, when advancement and social position are presumably based on merit, Cameron and his shadow government look like throwbacks to a bygone era.

Start with the boss himself: a stockbroker’s son with a £1.1 million home in Kensington, he’s a product of Eton, the grandest of all British private schools. Three of his cabinet ministers are also Old Etonians, as are at least 15 other top members of his team, from his election-campaign chief to his senior speechwriter. Britain may indeed be shaking off its old obsession with class–but such a toff-heavy squad hardly reflects the national profile. “Eton personifies world-class privilege,” says left-wing Labour M.P. Dennis Skinner. “The Tories have gone back to the snobs.”

Fair or not, the charge has a superficial merit. Eton (fees: £23,000 a year) stands out as a training ground of a governing elite. Founded in 1440, it has produced no fewer than 19 of Britain’s prime ministers, the last in the 1960s. And many of Cameron’s inner circle are members of strictly all-male London clubs. Like his father, he belongs to White’s, the oldest and snootiest of all, where members include the shadow chancellor, George Osborne (not an Etonian, but heir to a hereditary title as well as a furnishings fortune).

For a party still reinventing itself, some fear that impression could be damaging. “I don’t think it’s wise to reconstruct this kind of rule by cabal,” says Old Etonian Nick Fraser, author of a recent book on the school. “After two or three years in government, people may turn around and say your government is stuffed with toffs.” Cameron’s oh-so-modern commitment to the environment and public services may be heartfelt. But there he was last week, resisting conservative allies bent on slashing taxes–which might have been taken as evidence of old-style moneyed favoritism.

To many, Margaret Thatcher remains the Tory standard-bearer. A grocer’s daughter educated at state schools, she laid heavy stress on meritocracy, preferring like-minded ideologues to grandees. Her successors have usually worked hard to shed the vestigial image of well-born aloofness. (Sometimes a bit too hard: party image makers cringe at the memory of Tory leader William Hague’s flirtation with the baseball cap.) Still, Cameron may well be right in betting that Britain has outgrown such sensitivities. Nor does a posh upbringing any longer suggest isolation from the social mainstream. According to one recent survey, voters see Cameron as more “in touch” than either Labour Prime Minister Tony Blair or his likely successor, Gordon Brown.

Cameron may also be right about Britain’s newly meritocratic spirit. “Maybe Thatcher and her successors so comprehensively destroyed the association between privilege and the party that the privileged elite were able to repopulate the shadow cabinet without attracting much notice,” says William Nelson of the Future Foundation, a London think tank. “It may be that when choosing our political leaders we now look for the right people for the job, regardless of how they came to be there.” Rising wealth and the shrinkage of the blue-collar work force have blurred old distinctions. A study earlier this year by the Future Foundation found that 38 percent of the British consider themselves middle class. Extrapolating current trends, the figure will top 50 percent by 2020. “This is the greatest change in the country’s class structure in the last 1,000 years,” says pollster Bob Worcester.

Meanwhile, the always-shaky link between class and money looks weaker than ever. However defined, class can no longer be a good guide to likely voting habits in a country where one in three bank managers defines himself as working class. “Tribal voting has disappeared,” says Vernon Bogdanor, professor of politics at Oxford University, who tutored the young Cameron. “People are much more likely to vote on the issues.” That said, the Conservatives are taking no chances. The next election could be close, and just a hint of old-style privilege could alienate a few thousand crucial voters. The man who would be Britain’s next P.M. will thus continue to do everything he can to present himself as a man of the people–or at least not as a dry blueblood. On his guest list at the House of Commons last week: the Chicago rapper Rhymefest. If class doesn’t matter, attitude may.