A headhunter I bumped into last year told me about the difficulty she'd had in finding suitable staff. That week she'd taken a candidate with excellent paper qualifications for a meal. Which was where it all went wrong. "His manners were just unspeakable. Shovelling food on to his fork with his fingers. Talking with his mouth full, but holding his hand over it. Licking his fingers." And that was that. "My business is done over lunch. That's where you persuade people and do deals. I can't employ someone if people won't want to eat with them."

Had she told him why he hadn't got the job? Of course not. He'd been let down with polite lies. He would never know that something so apparently trivial had such significance. And perhaps what the headhunter really suspected was that if his manners didn't fit, he'd also be unaware of a myriad subtle rules about how to socialise and negotiate in the group he wanted to join.

The headhunter's story was in my mind when I read Alan Milburn's report on why the professions remain so hard for people from other classes to break into. Milburn sees what it has taken the government a long time to understand: that expecting mobility to improve just by getting more of the less privileged to pass more exams is a delusion. Social barriers are more complex, as are employers' priorities. Yes, they want qualifications. What they prize most, though, are more elusive social skills: articulacy, tact, team-working. Those words all describe much the same thing – an employee who can get along with, and be understood by, those around them. Employers want people who can understand their business's social codes.

The existence of different social codes makes attempts at social mobility precarious. There's much talk of Britain being more egalitarian and multicultural. In reality it remains deeply hierarchical. The dominant culture is that of the white middle class; the elite culture is that of the upper middle. Anyone who hopes to be socially mobile has, by definition, to learn to read a culture that is not the one they grew up with. Otherwise, no matter what their formal qualifications, they will either fail to get in, or fail to progress. In essence, they are emigrating from one kind of life to another, but our pretence that these barriers no longer really exist means they often emigrate without a map.

If our children were business people there would be none of this embarrassment. The net has hundreds of guides to working in different cultures. Keep quiet and drink a lot of coffee in Finnish meetings; expect the Dutch to be quick and abrasive; establish a personal relationship with the French first. Americans coming here are advised not to talk about their long hours or high pay. Instead, they're told, senior British executives prefer to convey the impression of a cultured and leisured elite. Discuss arts and current affairs at dinner parties, rather than business; even an official lunch is not expected to address the purpose of the meal until it's nearly over.

International companies are frank and practical about class and culture because profits depend on employees fitting in. Here, where our own internal migrants' lives and hopes can be shattered by such misunderstandings, we often keep expectations opaque.

The Milburn report sidles around this issue. In some ways it's sophisticated. It recognises that poor children increasingly lack the soft skills employers seek, because neither families nor schools provide the sporting and cultural activities that help to build them. It wants to encourage aspiration through more mentoring, particularly e-mentoring, and internships. But it doesn't talk about the painfulness of attempting to leave one sort of life behind, of the psychological risk involved in trying to establish another. It doesn't see that ambition and opportunity together still don't guarantee success. It doesn't see that without guides to spell out what's needed in a workplace, and in socialising outside it, a child from Moss Side is unlikely to profit from a fortnight in a City law firm in the way an Etonian would.

If social mobility is to be more common, children and teenagers must have real emotional support coupled with practical knowledge of what's expected of them. People working on the frontline of social mobility know it. In London's East End, where graduate unemployment is much higher than average, the Young Foundation is running successful short courses, teaching social and interviewing skills. In west London, William Atkinson, the inspiring head of a school with a very deprived intake, says that it's essential that pupils understand the dominant culture. He introduces them all, whether future doctors or gardeners, to great literature, theatre, art. He expects a work ethic. He tells his pupils that street culture is fine for home, but that it's joining the dominant culture that will give them choice.

More schools need that honesty and drive. Teenagers need to spend time with adults outside their social groups as mentors, friends and employers. And we need to find a way to talk about behaviour, manners, codes. Not because one set is better than another, but because it's the way humans recognise their groups. Pretending rules don't exist or matter only has one result – it freezes social mobility, and entrenches elites.