By the sound of things, David Cameron is getting ready to sack the Cabinet.

He means to put his children into state education, end private healthcare, dispose of his trust funds, and strip his father-in-law of that peerage. Once they get rid of their inherited wealth, Dave and his wife, Samantha, will move to a council house and try their hands at social mobility.

This was what the Prime Minister meant, surely, when he said the other day that he agreed with John Major. The former Conservative PM had described the dominance of a privately educated middle-class elite in British life as "shocking". For good measure, humble Sir John remarked in a speech: "I remember enough of my past to be outraged on behalf of the people abandoned when social mobility is lost."

Asked about all of this, Cameron offered what sounded like unhesitating approval: "You only have to look at the make-up of the high levels of Parliament, the judiciary, the army, the media. It's not as diverse; there's not as much social mobility as there needs to be."

Warming to his theme, the Prime Minister let his rhetoric take wing. "What I want to see is a more socially mobile Britain. I want to see a Britain where no matter where you come from, what god you worship, the colour of your skin, what community you belong to, you can get to the top in television, the judiciary, armed services, politics, newspapers."

Now let's allow, to begin with, that this pair of stout Conservatives describe the reality of 21st-century Britain accurately enough. In the fields Cameron mentions, and in several others besides, one small segment of society - one class, if you prefer - is utterly dominant. Independent schools might well be peerless (at those prices, they ought to be). But it is strange indeed that a sector educating only 7% of children has managed to turn so many professions into reserved occupations for its clients.

Or perhaps it is not so strange. What Major was describing, and what Cameron was acknowledging, was a carve-up. Social mobility has not been "lost" thanks to an accident or political carelessness. The elite, politicians included, have set up a reserved lane on the road through British life. It helps them gain the wherewithal to pay the tolls and ensure that their children enjoy the same untroubled journey, reaching the same destinations.

None of this is exactly news. In fact, it is familiar enough to be called traditional. Major is troubled only because he came to maturity during that brief period, roughly from the 1950s to the 1970s, when Britain was supposed to be changing; when origins were no longer supposed to be tyrannical; when any walk of life, from politics to the arts, journalism to academia, was believed to be open to all. Meritocracy, some called it. Others of us knew it as a fair fight.

That's over now. One by one, the doors have been slammed shut. The old elites have discovered a new, brazen confidence, especially in the purchase of advantage through education. Private schooling and the Oxbridge PPE degree - Cameron knows all about those - are passes to the fast lane again. In England, tuition fees have restored the power of money and class. As the excluded know only too well, what the elite has it holds, at all costs.

It has come to something, though, when Major, the erstwhile ­Brixton boy, is naming a scandal. The argument breaches the bounds of plausibility when Cameron - the Old Etonian epitome of the dominance Major bemoans - is nodding in agreement. These are Tories, for pity's sake, of a type inclined to doubt that class is ever a barrier to hard work and merit. Yet they cannot deny what has been going on when even institutions they dislike, such as the BBC or The Guardian newspaper, are stuffed with the children of the elite.

Neither man would be mistaken for a deep thinker. They would bring chaos down upon their political world, in any case, if they started drawing too many conclusions from the facts under their noses. But take the very phrase "social mobility". Cameron and Major both seem to think it is some sort of shorthand for the spoils being spread more widely. The Prime Minister identifies it as a key to "diversity", to allowing more people from backgrounds unlike his to "get on". Tories often pay lip service to the notion.

But this is to misunderstand the term. Implicit in the idea of true social mobility is the sticky fact that some will fall while others rise. What else could be involved? Eton and Brasenose College for all? That would devalue the currency. It would confer no advantage on the sort of people who look to Cameron to preserve their comforts. It would ruin everything. It would never do.

Take one example. The Coalition Cabinet is full, notoriously, of the products of the public schools. The 7% have colonised the heart of government to a statistically improbable extent. Of the 33 people called upon to sit around the big Downing Street table, 18 have experienced private education. So how many of these, and which ones, would Cameron like to dump in the name of diversity? How would they feel, given the sums invested in their schooling, if they lost out to the socially mobile?

The Cabinet counts as both a microcosm and a prime example of the phenomenon Major was bewailing. Yet how else could the Prime Minister's dream of diversity work? Either he would have to remove privileges from a few or grant equality to all. What are the chances?

Last week, while confessing that progress has been too slow, Cameron boasted of extra money going to schoolchildren of poor families, free childcare for toddlers, the free school movement, and rising numbers (allegedly) of university students from deprived areas. Some of these measures have value, each is a species of tokenism. To do more, to ensure that class and origins counted for nothing, would wreak havoc on Planet Tory.

Cameron and Major are not ­interested, then, in raising all boats. They want a few to get on, but not all. For their kind of mobility to work, the great mass of people must stay pretty much as they are. In a Tory world there has to be a lot of failure to give a meaning to success. It goes to the heart of a particular understanding of human relations. What lay behind the lip service was an uneasy sense that too many voters are catching on. A class-ridden society has become a rigged society.

The beneficiaries, even when they style themselves "liberal" or "progressive", understand this fact only too well. They might wish it otherwise, at least in benign theory, but you can judge them by the choices they make for themselves and for their children. At every turn, they talk as though there is no choice.

They got ahead and mean to stay ever further ahead, no matter what it takes. They can rest easy, though, in the knowledge David Cameron is the last person liable to change the rules. He's one of them, after all.