The chief executive of Tesco, Britain's largest private employer, has issued a warning: are kids dont no nuffink. Terry Leahy said this week that our educational standards are "woefully low", and that young recruits to Tesco often have to be taught basic literacy, numeracy and communication skills before they can be unleashed on the aisles or stockrooms.

He's not alone. This warning rumbles across the country. A friend of mine is an academic at a middle-ranking university, and she recently showed me some of her students' essays. "It's quite normal for them not to know how to use paragraphs, or commas, or to be able to spell," she said, shaking her head. Some are barely literate, despite a clutch of A-levels. She found the same at two other universities.

It's not enough to glibly announce that there's no problem, as the Government did this week. Yes, a Chicken Little cry that educational standards are plummeting echoes across every age: one of the oldest tablets ever discovered in an archaeological dig warns that the kids of today aren't what they use to be. Yes, there are still a lot of good schools. Yet there are more children getting into Oxbridge every year from the pool of 300 kids at Eton than from the 300,000 kids on free school meals. Either you believe those Etonians are born smarter – an absurd proposition – or our school system is failing poor children on a vast scale. How many great minds are we allowing to atrophy just because they weren't born to wealth?

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It doesn't have to be like this. A far better system is possible; we just need to follow the evidence. And the road-map runs through – of all places – North Carolina. Something extraordinary has been happening in the state's schools over the past few decades, and the best guide to this experiment is an important new book by Professor Gerald Grant called Hope and Despair in the American City: Why There Are No Bad Schools in Raleigh.

He looks at two very similar cities – Syracuse in New York State, and Raleigh in North Carolina. They are both 1950s boomtowns turned to 1980s ghost towns. It's the same-old, sad-old story: industry shrivelled and the white middle classes stampeded to the suburbs, leaving behind shell-cities scarred by poverty. Yet there is today an extraordinary gap between these cities. In Syracuse, only 25 per cent of 12-year-olds can read, write or do arithmetic to the appropriate basic level – while in Raleigh, it is 91 per cent. Almost all of the schools in Syracuse fail; none of the schools in Raleigh do. What are they doing differently?

Raleigh's governors decided to do something bold and unconventional: they looked to the scientific evidence. In 1966, Professor James Coleman was commissioned by the White House to conduct the largest study, to that time, of what makes good pupils succeed and bad pupils fail. After years of on-the-ground analysis, he came up with something nobody expected. He found that the single biggest factor determining whether you do well at school or not isn't your parents, your teachers, your school buildings or your genes. It was, overwhelmingly, the other kids sitting in the classroom with you. If a critical mass of them are demotivated, pissed off and disobedient, you won't learn much. But if a critical mass of them are hard-working, keen and stick to the rules, you will probably learn. Watch any 10-year-old: they are little machines for snuffling out the sensitivities of their peer group, and conforming to them.

Facing their schools' failure in the 1980s, the Raleigh school board returned to this evidence and tried to puzzle out: how should it change the way we run our schools? Touring the schools, they could see why the research was right. Children from poor families need more help than kids from rich families. They are more likely to have chaotic home lives, less likely to have the importance of education drilled into them from birth, and they have lower expectations for themselves.

In small numbers, in an ordered environment, these poor children can quickly be brought up to the level of the rest, and indeed exceed them in many cases. But when they form the majority of a school's pupils, the teachers can't cope, discipline breaks down, and learning stops. A school for poor children soon becomes a poor school.

So they formulated a bold – and strikingly simple – solution. They wouldn't allow any school, by law, to have more than 40 per cent of its children on free school meals, or more than 25 per cent of children who were a grade below their expected level in reading or maths. Suddenly, the children who needed the most help wouldn't be lumped together where their problems would become insurmountable; they would be broken up and fanned out across the educational system. Raleigh merged its school system with white suburban Wake County, so they became one entity, sharing pupils. In order to soothe suburban suspicion at this change, Raleigh turned a third of its inner-city schools into specialist academies, offering excellent music or drama or language specialisms. Soon, children were bussing in both directions every morning, in and out of the suburbs.

Many conservatives savaged the plan as "social engineering" and said it was doomed to fail. Some parents were angry, and a few decamped for the private school system – until the results came in. Within a decade, Raleigh went from one of the worst-performing districts in America to one of the best. The test scores of poor kids doubled, while those of wealthier children also saw a slight increase. Teenage pregnancies, crime and high school drop-out rates fell substantially.

It's not hard to see why. Each school had a core majority who respected the rules and valued education – and the other kids normalised to their standards. Those who found it tough could now be given special attention, because they weren't any longer surrounded by a mass of equally troubled kids. Today, 94 per cent of parents in Raleigh say they are happy with their child's education. School boards supporting this integration keep getting re-elected.

Raleigh succeeded because it built genuinely comprehensive schools: in which rich, middle-class and poor kids learned together. In Britain, we tell ourselves we have built "comprehensives" – but, except in a few enclaves, we have done nothing of the sort.

We allocate school places according to how close you live to a school. This immediately creates a social apartheid where middle-class children have successful schools in leafy suburbs, while poorer children are ring-fenced in sink schools and end up at Tesco at 16 with few useable skills. (Rich children are creamed off entirely into private schools.) Comprehensivisation didn't fail; it didn't happen.

There are only a few areas in Britain with genuinely mixed schools, like Grampian – and they get the best overall results. At the opposite end of the spectrum is Kent, where children from the middle and the rich are creamed off into grammar schools in which just one per cent of kids are on free school meals. They have the worst overall results in the country.

So we know how to make schools work: integrate them. Occasionally, our politicians take a tiny step that brings us closer to this. The Labour council in Brighton allocates school places by lottery; the Tories say they will abandon catchment areas, letting a few poor kids slip through. But both only tinker at the extreme social segregation that crowbars apart the educational system.

Integration is a good policy for bleak recession times since it delivers dramatic improvements at little extra cost. Raleigh actually spends less than the US national average on its schools, and 25 per cent less per pupil than failing Syracuse. In the long term, integration actually saves us a fortune in welfare payments and prevented crime.

Yes, the right will scream at first that it is "an attack on the middle class". In fact, it is a great compliment to the middle class: it wants to use their children and their values as the sun around which every child's education revolves. Yes, some parents will scream that they don't want their kids being taught alongside "chavs" and "pikeys". This should be called out bluntly – it is bigotry.

A democracy is based on a bargain: every child gets a chance to succeed, whatever their background. Today, we are breaking our deal. We are leaving millions of children to fail, just because their parents didn't have money. Do we want to be a country where our children are sorted at five into different playgrounds according to Daddy's bank account? Do we want to be an place where rich children only glimpse poor children from the car window as they are driven to their better, plusher school, and their better, plusher lives? Or do we want something better for our kids?

Our politicians insist that "we're all in this together". This will only be true if – at last, and at least – our children go to school together.

j.hari@independent.co.uk