Every era produces politicians who seem to sum up the spirit of their age – and in our own case, the most perfect example might be the Tory cabinet minister Jeremy Hunt.

Having been the accident-prone culture secretary, he is now in charge of the NHS, and facing the first stirrings of an A&E crisis. But there is good news for him, too. Last week, with Hunt's personal worth already estimated to be around £5m, it was revealed that a company he founded 17 years ago – which now trades as Hotcourses, and works as a kind of online education search engine – is on the verge of being sold to a private equity firm. It will net him somewhere in the region of £17m. His life, then, is almost surreally comfortable – as befits a stereotypical member of the modern elite who was the head boy at Charterhouse (current annual boarding fees: £32,925) and went on to be a contemporary at Oxford of David Cameron and Boris Johnson.

Hunt's social tribe, needless to say, dominates the cabinet. Recent figures based on current and previous salaries, shares and property suggest that two thirds of senior ministers are millionaires, with Cameron and his wife Samantha – the daughter of a baronet – thought to be in line for an eventual inheritance windfall of £25m. And though some who sit around the cabinet table came from state schools (the foreign secretary William Hague is a good example), there is still something remarkable about how many of the top political jobs are currently held by people who went to some of Britain's major fee-paying institutions: among them, the prime minister, the deputy prime minister, the chancellor, and the mayor of London.

Then, of course, there is the Eton factor, which encompasses not just Cameron and Johnson, but plenty of their Tory colleagues, aides and advisers. Cameron's chief of staff is an Old Etonian, as is George Osborne's chief economics adviser. The Cabinet Office minister Oliver Letwin is too, along with the Tory chief whip, George Young, and the chief of the Downing Street policy unit – Jo Johnson, younger brother of Boris.

Despite the fact that around only 7% of British children are privately educated, 34% of MPs went to fee-paying schools, and the figure for Tory members of parliament is 54% (the Labour figure, to put that in perspective, is a mere 12%). People who have had expensive educations dominate journalism, law, finance – and, of late, even the supposedly meritocratic powerhouse that is British pop music (witness Mumford and Sons, Florence Welch, Lily Allen, Laura Marling et al). "It is remarkable how many positions of wealth, influence, celebrity and power in our society are held by individuals who were privately educated," said the education secretary, Michael Gove, in May last year.

Now, another voice has joined the debate. Last Friday evening, John Major – the former Tory PM, who famously left his south-London state school at 16, with only three O-levels – spoke at a dinner organised by the South Norfolk Conservative Association. Having already unsettled the government with his call for a windfall tax on energy firms and worries about "lace curtain poverty", this time Major focused on the upmarket backgrounds now shared by the people at the top. He tried to blame the last Labour government for a "collapse in social mobility", which does really not chime with the facts, but his basic point was simple enough: "In every single sphere of British influence, the upper echelons of power in 2013 are held overwhelmingly by the privately educated or the affluent middle class," he said. "To me, from my background, I find that truly shocking."

Major's revival as a Conservative elder statesman is fascinating to behold. His torrid experience of power and the shambles into which his government fell seem to be fading memories: far more important, it seems, is the huge contrast between his background and bond with Tory voters, and the current Conservative leadership. Somewhere in the party's collective soul, perhaps, is a yearning for the days when they could put their leader's face on an election poster, and accompany it with a winning pitch to voters: "What does the Conservative party offer a working class kid from Brixton? They made him Prime Minister."

As the kerfuffle about Major's comments proves, there are two connected elements in this story. One is bound up with almost the entirety of public life and culture more generally, and the renewed dominance of people from a very small range of backgrounds, from Coldplay's Chris Martin to the Eton-educated archbishop of Canterbury.

The other is specifically about the Conservative party, and the way that a political force that had long found its leaders among the self-made and state-educated has reverted to type, and what that means for the Tories' prospects. Of course, compared with the days when 172 of 415 Tory MPs came from the aristocracy (as was the case in 1935) and the share of privately educated Conservative MPs exceeded 70%, the party can now claim to have embraced openness and meritocracy. But at the top, things seem to have gone backwards, reflecting that wider sense of the brazenly privileged and wealthy returning to the national foreground in a way that might once have seemed unthinkable.

Cameron, let us not forget, is the first privately educated Tory PM since 1964 – and to give the story even more piquancy, he won the leadership battle after facing off against David Davis, who was raised on a council estate, educated at a state school, and spent 17 years rising through the corporate hierarchy of the sugar firm Tate & Lyle. Had Davis become Conservative leader back in 2005, things might have been slightly different; certainly, his take on the current state of Tory play was crisply summed up in advice he threw Cameron's way earlier this year: "No more Etonian advisers".

John Major: the former Tory PM has lambasted the dominance of the privately educated elite. Photograph: David Hartley/Rex Features



So, what happened? How did the party once led by the state-educated Edward Heath, Margaret Thatcher and Major revert, so spectacularly, to type? And what does the private-school domination that Major has decided to decry say about the kind of country Britain has become?

The renowned historian David Kynaston is the author of three near-definitive histories of the postwar UK, Austerity Britain, Family Britain and Modernity Britain and, as it happens, an alumnus of the fee-paying Wellington College, with a penetrating take on what Major has been talking about. Both Britain and the Conservative party began to turn away from the public-school elite in the early 1960s, when two things were happening: the demise of deference and the blurring of old cultural divides; and an increasing sense that the UK's decline was being worsened by the rule of gentleman amateurs – and, perhaps, what George Orwell called "the decay of ability in the ruling-class".

The Tories, he says, took a while to wake up. "There's the astonishing thing that when Harold Macmillan went in '63, they appointed another Old Etonian to be prime minister, in Alec Douglas-Home. In all logic, he should have been trounced at the next election by the meritocratic Harold Wilson, but he actually gave him quite a close race, which perhaps shows you how small-c conservative Britain still was. But, nevertheless, once he goes in '65, it moves to Heath. And Heath actually came from a pretty poor background – which, at the time, seemed really important and symbolic.

"I grew up through all this," Kynaston goes on. "And, for years and years, it seemed inconceivable that the Tory party would ever go back to having an Old Etonian as leader." Society, he points out, was becoming more equal up until the late 1970s, and Britain was also seeing "the semi-collapse of the old cultural hierarchies". How much social mobility was happening became perhaps over-rated, he reckons, but there was a clear sense of positions of power and influence opening up as never before.

After Heath came the legendary grocer's daughter Margaret Thatcher. Public-school Conservatism obviously endured (there were six Old Etonians in Thatcher's first cabinet), but it was offset by the kind of self-made Tory politicians who could speak to working-class voters as a matter of instinct – not least the "Chingford Skinhead" Norman Tebbit, a state-educated former airline pilot. Meanwhile, things at the top of the educational hierarchy were quietly changing, in keeping with the retrospective sense of a small elite becoming detached from society as the free market was allowed to let rip.

"The private schools got their act together," says Kynaston. "They became these incredibly sophisticated kinds of marketing organisations. And they became so highly resourced. Now, fees have increased well beyond inflation. The facilities are fantastically impressive. You now get articles in the Spectator, grumbling about the money required." He also agrees also that privately educated people found a new, demotic voice – think about that alumnus of Fettes College, Tony Blair, with his glottal stops lately imitated by George Osborne – that served to smooth over their origins, and create the impression that the old grouse-moor stereotypes were a thing of the past.

As it has turned out, though, there is a public sensitivity about senior Tories' backgrounds that will not go away, no matter how many slightly anxious Cameron soundbites (eg "What counts is not where you come from but where you are going", the line chucked at journalists by the PM's spokesman yesterday) are dreamed up to deal with it. It was surely a factor in his failure to win an election even against the clapped-out Gordon Brown; and three years on, it may partly explain the fact that the Tories cannot seem to correct their ongoing lag in the polls.

One outer-London Labour MP recently told me that erstwhile working-class Tory voters in his seat "seem to look at Osborne and Cameron and think, 'Who are these people?'" To quote from a recent story in the Daily Telegraph, "only 29% of voters now think Cameron 'understands people like me', as opposed to 65% who disagree, with the prime minister's Eton background continuing to create a perceived gulf with ordinary people".

To some Tories, this is a matter of mild irritation. Others, though, have sounded positively furious – as evidenced by the now-legendary words of the Tory backbencher Nadine Dorries, a native of inner-city Liverpool, whose father was a bus driver. In July 2012, let us not forget, she said: "There is a very tight, narrow clique of a certain group of people and what they do is act as a barrier and prevent Cameron and Osborne and others from really understanding or knowing what is happening in the rest of the country. I think that not only are Cameron and Osborne two posh boys who don't know the price of milk, but they're two arrogant posh boys who show no remorse, no contrition, and no passion to want to understand the lives of others – and that is their real crime."

David Cameron and David Davis battled it out for the leadership of the Tory party in 2005. What would be different now if Davis had won? Photograph: David Jones/PA Archive/Press Association Images

So, will the Tories eventually realise their error, and resume their tradition of picking leaders with more ordinary backgrounds? "My gut feeling would be yes, they will," says Kynaston, who doesn't fancy the chances of their assumed leader-in-waiting. "It would seem pretty unlikely that they would actually go for Boris Johnson as the next leader. I think it'll go back to the old pattern: Heath, Thatcher, Major, Hague. Unless Cameron wins at the next election, all this will be seen as a big reason why he failed to connect. It'll be interesting on the Labour side, as well – whether they ever again have a privately educated leader. I think it's most unlikely."

Within Conservative politics, there seems to be a mounting understanding of all this. Among the ever-increasing number of internal Tory groupings, there is now a pressure group called Blue Collar Conservatism, pledged to "widen the Conservative base and transform the lives of ordinary voters". This year has also seen the arrival of Renewal, an impressive set-up which talks about reinventing the Tories as a "workers' party". Their founding document bemoans the fact that the parliamentary Conservative party "still comes from a relatively narrow social base", and at their launch party in Westminster in July, among the posters on the wall was the aforementioned John Major effort from 1992: "proof that the Conservatives have both attracted working-class voters," said the official blurb, "and have promoted working-class leaders in the past".

Renewal's founder is an influential Tory thinker, David Skelton, the former deputy director of the Conservative thinktank Policy Exchange. He is the son of a teacher father and a mother who worked in a shop, and he went to a comprehensive school in County Durham.

"The point John Major is making is that we've got a long-term problem," he says. "Lots of institutions are dominated by people from a very narrow background: the judiciary, business, the media, politics." The Tories, he adds, have to be "pro-active about getting people from low-income, working-class backgrounds into politics". As he sees it, they need to sell their education policies as a matter of widening opportunities, and "ensure there are people from those backgrounds on its benches".

I have spoken to Skelton before: when reminded of the fact that there has been such a counter-revolution at the very top of the party, he becomes evasive. And so it proves today: "I obviously think that more needs to be done, to appeal to all kinds of voters – working-class people, people in the north, people in cities – who still aren't voting Conservative in nearly large enough numbers," he says. The party, he reckons, is making "big steps in the right direction", and he mentions not just what is happening in schools, but the recent reshuffle, and the promotion of such ascendant talent as the Keighley MP Kris Hopkins, and the new welfare minister Esther McVey, a state-educated Liverpudlian. "The more working-class voices there are, the better," he says.

A direct question, then. Will the Heath-Thatcher-Major line of state-educated Tory leaders eventually be resumed?

"I would say that it doesn't really matter what school people went to providing they have the right policies," he says. "But, yeah … of course, there will be state-educated Tory leaders in the future."

A pause, for emphasis. "Of course there will."