The other night I met Florence who, although suspended from school, made homeless at 15 and then sensitively rehoused in a hostel for junkies, has just completed the first part of a psychology degree at Oxford University. “With a 2.1!” she says, pumping a fist. Tall and black, stroppy and beautiful, she is no one’s positive action show pony.

“Oxford is not my life’s dream,” she says drily. “No one really likes me there.” Too many students are snobby; they don’t get her music; some say that they find her scary; she has few friends.

I meet George too. His mother left him at 13; he fell out with his dad at 15, and, abandoned to the South London streets, started dealing drugs. He was, he smiles, very good at it: disciplined, savvy, adept at side-stepping trouble. With his understated cool and desire to break into legit business, he reminds me of Stringer Bell in The Wire. Except that Stringer was blown away in a gangland feud and George is finishing a finance degree at Queen Mary, and just had a placement at Deutsche Bank. Perhaps because he has survived alone for so long, George is rather solitary. If he slips into street talk his fellow students stare, and, while he is more tactful about them than Florence, he finds limited common ground.

He is amazed, even amused, that they were all so “incredibly spoon fed”. Florence and George were at a dinner receiving awards from Kids’ Company, a charity of rare imagination that scooped them up and believed in them when their own families failed.

As Alan Milburn concluded this week in his report on the difficulty of children from even average backgrounds breaking into the top professions, many children need a surrogate pushy parent. But what it did not say was how resilient a child must be, possessed of determination and ambition flecked with defiance, to gain citizenship in that unknown and hostile land, a different class. No wonder so many are discouraged before they even reach the border.

Mr Milburn describes the emergence of a “not for the likes of me” syndrome, not even dreaming of a career in law or medicine. I was reminded of my final months at journalism college. Everyone else was applying for BBC traineeships: to me, the first generation of my family to go to university, the BBC was something we watched from the sofa. That I might work for it truly never crossed my mind.

When my colleague Alice Thomson wrote this week that you don’t have to be middle-class to be a pushy parent, I really had to laugh. How can you push when you can’t see where you’re going? My folks, who left school at 14, could teach me to read and encourage my studies, but the arcane rules of the educational system were beyond them. (And that was before the terror of debt from student loans.) As one child interviewed for the Milburn report said: “My parents don’t know anything about the application process and it is difficult to understand alone.”

Even as a middle-class parent myself, I find this sharp-elbows business difficult, the system opaque. It takes intense application to work out what standard a child must reach at each point and how, by constantly bothering teachers or hiring tutors, to resolve all shortcomings.

Meanwhile, there is always some other mother, invariably non-working and vaguely hysterical, who is five smug moves ahead. And to think our pushing days are not done when that Ucas form goes off, but only after we have called in the vaguest favours to blag our darlings a tea-making stint at Goldman Sachs.

It is not only children from inner-city hoods such as Florence and George, but those in ordinary, provincial families who must rely, mostly, on luck. No one else will fan your slightest spark of potential. You must pray that a teacher reminds you that if you’re thinking of medicine you need chemistry A level. Or that someone with foresight and spirit tears up your diligent application for teacher-training and propels you instead into an unimagined future. Working-class kids are mocked for craving to be reality-TV contestants, but unlike the Bar, at least The X Factor’s entry process is clear.

It is the inflation in middle-class life, exploding house prices and school fees, besides a new keepy-uppy consumerism, that has made clinging to those high-paid professions even more vital. And the expansion of higher education has mostly benefitted middle-class girls.

I suppose my feminist soul should rejoice. But actually I am more dismayed that now second-rate, educationally force-fed children of both sexes consign the brightest poor to jobs beneath their brain power, and incomes below their deserts.

Mr Milburn’s report has some fine ideas for redressing this injustice, but they come a decade too late and will no doubt be swept away by a Conservative Government untroubled by the haute bourgeois closed shop.

That the Government’s “gifted and talented” programme is running in only 8 per cent of primary schools — mostly ones with a bulging middle-class catchment anyway — is a disgrace. But new Labour has long had trouble with the notion of creaming off the elite, scenting a whiff of eau de grammar school. They call a maths book full of ticks a success when it shows only that the sums are too easy, the child bored.

Yet how else can we help those Florences and Georges, except by separating them from mocking, work-shy peers and solemnly explaining that they have a talent they must not waste. They should be scouted as football clubs find young talent. Give them extension papers, extra reading, pack them off to summer schools to hear speakers on philosophy, history, politics. Get them debating. Take them into merchant banks and newspaper offices. Expand their world.

Compensate for the absence of those quotidian details of a middle-class education: trips to museums, chit-chat about books, serious newspapers.

And, yes, as Mr Milburn proposes, focus on the “soft skills” too. Tell them how to deal with jerks who mock their grammar, wonder why they don’t ski, ride or speak Italian. Explain that someone who is smooth isn’t necessarily skilful. Tell them they are entitled to be there. Teach them to tap in to their hunger and drive, their street smarts, the benefit of a unique and unrepresented point of view. That it’s not a chip that kids like Florence and George carry on their shoulders: it’s a jetpack.

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