The driveway leading up to Wellington College is a kilometre long and cuts through a vast green blanket of lawn, the edges of which have been cordoned off to ensure the damp grass is not trampled by careless feet before the end-of-term rugby match. Walking up the long drive, there is ample opportunity to admire the impressive red and white brick building as it emerges from the early-morning mist. As you get closer, you notice the carved stone pediments silhouetted against the sky.
Established in 1859, the college was founded by Queen Victoria and the Earl of Derby as a national monument to Britain's great military figure, the Duke of Wellington. It is a school that exudes privilege from every pore, with its 400-acre grounds, its golfing greens, its shooting range and its extensive stretch of private woodland. A term as a boarder at Wellington costs £8,975, and last year there was a 100% A-level pass rate. The school's motto, inscribed in Latin in the chapel hymn books, is Heroum Filii - Sons of Heroes.
Chris Uthman, 15, is the son of a truck driver and an Accident & Emergency nurse. He lives on a council estate about four miles south of Manchester city centre with his mother - his parents split up when he was six. Until relatively recently, Chris went to school at Chorlton High, a comprehensive where fewer than half the pupils are white British and a high proportion have English as their second language. In 2008, it was given a "satisfactory" rating by Ofsted.
When he was 14, Chris was excluded from his school. He had been playing truant from lessons for more than a year and had fallen out with a new maths teacher. It came to a head one day in the classroom and Chris became verbally aggressive. He is a broad-shouldered teenager, well over 6ft and with an expression of glowering discontent on his face that he adopts whenever he feels threatened or uncomfortable. It is easy to see how Chris could appear intimidating.
He says he regrets it now. "I took it a bit too far," he says, shaking his head. "I felt bad. How stupid was I? It was dumb. It could have been a minor situation and I could still be in school. My mum wasn't happy with me at all."
We are sitting at a large table in an airy conference room in Wellington with windows overlooking a cobbled courtyard. Girls in tartan skirts and boys in well-tailored suits walk past hurriedly on their way to lessons, carrying lever-arch files neatly labelled with their teachers' names. Winter sunlight streams through the panes of glass. Today, Chris Uthman, a boy without a single academic qualification to his name, has come to Wellington to see how the other half goes to school.
He is part of a ground-breaking partnership forged between Wellington College and Cool UK, a youth project based in Burnley, Lancashire, that gives vocational training to young offenders and teenagers who have fallen by the wayside of mainstream schooling. Some of them have, like Chris, been excluded. More often, they will simply have dropped out because the conventional school system did not meet their needs. A proportion of them end up in care.
"If your mother's an alcoholic and you've been up all night holding her head while she vomits in the toilet, then you're not going to be awake the next day at school," says Mike Dunn, one of the organisation's youth workers. "You're not going to react well to a teacher screaming at you to do things. Those are the kind of kids we get."
Chris agrees. The problem with traditional schooling, he says, is "the rules and all that. You might go home at the end of the day and have no rules at your house and be allowed to stay out as late as you like. Then, at school, that gets a detention. So the kid asks: 'Why bother? I'll just wag your lessons.' But school has to be done. If you act like I did and learn nothing, that's the end of you. You're on the dole for the rest of your life."
For 48 hours, Chris and two other adolescents with troubled personal histories have been invited to become public-school pupils in order to experience education at its finest. These are children with few opportunities or role models, the sort of children that politicians assume will inevitably get involved with petty crime. These are the sort of children who, without guidance, would be blamed for the breakdown of communities; the sort of children many of us would cross the street to avoid. And these are the children who will be sleeping in dormitories, eating in the cafeteria-style canteen and sitting through the end-of-term carol service in the Wellington College chapel. In March, a group of Wellington pupils is expected to make the return trip to Burnley.
For Anthony Seldon, the master of Wellington, the scheme presents an alternative to the independent-school bursaries offered to less privileged children. "The problem with bursaries is that they cherry-pick, denuding the state schools of the brightest and best," says Dr Seldon, sitting on a sofa in his office, surrounded by school photographs and bowls of potpourri. "My philosophy is powerfully moved by a desire to build bridges between people of different social backgrounds, economic circumstances, races or religions. I believe we have to fight always a triumphalism of separateness, and I see this partnership as a way of trying to combat that and change people."
Although it is a deceptively simple idea, it is one that has never before been put into practice. If the scheme proves successful, it could provide a blueprint for other independent schools under pressure to demonstrate that they provide a public benefit worthy of their prized charitable status.
But, for the moment, Chris is not thinking of the wider ramifications. He has other, more pressing, concerns. "I need a cigarette," he says as he walks outside, shoulders hunched, hands in his pockets. He is wearing loose blue jeans and a grey sweatshirt, the hood lying flat against his ears like a monk's cowl. He does not put it up, despite the freezing cold. Instead, his face once again assumes its sheen of impenetrability, as if guarding itself against the unknown. Is he nervous? "No." I look at him sceptically. "It's just meeting new people."
Stephanie Booth is a slight woman with choppy grey hair and an air of contained vigour. As the development director of Cool UK, she devotes much of her life to looking after young people who find themselves on the margins of mainstream society. She would hate to be labelled a do-gooder. The thought of this scheme being called a "social experiment" makes her shiver with distaste. In fact, Steph does not have much time for labels of any sort: she finds them unnecessarily reductive and prejudiced. "To me, this project is all about challenging the labels that we put on people," she says, sipping on a polystyrene cup of coffee dispensed by one of the numerous Wellington vending machines.
She is understandably exhausted - the exchange scheme has been six months in development. Yesterday, she drove the 200 miles down from Burnley with Chris and two teenage girls, Donna Taylor, 14, and 16-year-old Grace Taylor (no relation). Today, she was up again at 7.30 for breakfast, calming frayed nerves and trying to soothe the pangs of adolescent self-consciousness. "We had to get photographic evidence of our lot awake at 7.30 in the morning," Booth says with a laugh. "Otherwise no one would ever believe it."
The Cool UK offices, located in Burnley and Manchester, provide vocational training in areas such as hairdressing, construction and motor vehicle maintenance. Many students arrive there with low self-esteem, an erratic approach to learning and limited aspirations for the future.
"We are the knot at the end of the educational rope," Steph says. "People looking superficially at the teenagers we've brought here today would judge them by their appearance and dismiss them as dropouts, but in fact all that divides them from the Wellington pupils is their socio-economic background. What we are trying to do is take them out of their backgrounds and make it irrelevant; to challenge each of the kids to meet others that they would never normally get the chance to know.
"Some of these Wellington pupils are destined to become high-fliers and captains of industry. How great would it be if, when they reached the top of their professions, they remembered they weren't just talking about employees, they were talking about lives lived?"
Steph knows better than most what it means to be in a position of power - she is the stepmother of Cherie Blair, who has given her backing to the project and is due to attend a Cool UK fundraising event later this year. "Cherie is a great supporter of what we're doing," says Steph. "But also, of course, I am her stepmother and she knows there'd be trouble if she didn't come along."
Although I am deliberately not told the more sensitive details of the children's family backgrounds, I learn that both girls come from broken homes: Donna has been in care and now lives with her mother; Grace is cared for by her grandmother. Their personal lives are precarious and fragile, defined more by uncertainty than anything else.
The first lesson of the day is a "street-dance" class for the two girls. We trudge several hundred yards down to the state-of-the-art sports centre, past the swimming pool, saunas and squash courts until we get to a large dance studio. A thudding hip-hop beat emanates from a sound system in the corner. A group of Wellington girls are being taught a high-speed dance routine by a teacher called Pandy, who looks far trendier than any teacher I can remember. "Do you want to join in?" she asks. Donna and Grace shake their heads in unison.
Donna, small and blonde and engulfed in an oversized grey sweater, is distinctly unimpressed. She scans the room with a dismissive gaze and squats down on the floor, hugging her knees into her chest, her Ugg boots squeaking against the varnish. Grace merely shakes her head with a tentative smile and takes a seat on the other side of the room. "They may look moody and petulant," Steph whispers to me, "but actually their attitude of 'I don't really care' is a cover for 'I really do care.'"
The surprising thing is that the Wellington pupils who have been assigned to look after Donna and Grace appear entirely non-judgmental and unfazed by the evident tension. Part of this is confidence. One of the most striking differences between the two sets of children is the air of poised self-assurance and maturity of the Wellington students, compared with the painful shyness of the Cool UK threesome. These are young people who have been told they can achieve and who feel supported enough to believe it. Ask them what they feel about the whole experience, and the Wellington pupils will have an eloquent, well-constructed response at the ready.
"It's nice to meet new people," says Georgina Singer, 16, who is studying for her International Baccalaureate and hopes to go to Oxbridge. "I think it's very easy for any boarding school to cut itself off from the outside world. But at Wellington, we're encouraged not to be boastful but to be grateful, and I really like that."
Tom Rowe, 17, adds: "I think everybody benefits from this experience. There are always going to be stereotypes - for public school pupils as much as for these guys - but I don't necessarily think that any of us meets the expectations or prejudices that other people have. It's important to have an idea of how other people live."
Back at the dance class, Donna and Grace are slowly beginning to thaw. It starts with a conversation about food. I ask them what they had for breakfast and Donna breaks out into an unexpected smile. "It were lovely," she says. "She [Grace] had eggs, beans and toast. I had a croissant and it was all free! They've got vending machines with chocolate and everything." Grace nods her head. "I'm starving. Is it break-time soon? I'd like to get a brew." Shortly afterwards they join in with the dance routine for the last 10 minutes of the lesson. Steph is beaming.
It is something of a breakthrough, especially for Donna, who has never been comfortable in a mainstream school environment and has a history of disruptive behaviour. "She is very bright," says Steph. "The thing is she has not yet made the connection between wanting a future and having to modify her behaviour to achieve it."
For Grace, the challenges are slightly different. "I used to love my school," she says, staring down at her unlaced desert boots that look too big for her feet. Her fringe, slightly too long, keeps getting in her eyes. "My favourite subjects were art and design and English." But her school, a state-run boarding institution near Warrington, closed due to lack of funding before Grace got any qualifications. Without anywhere else to go, she ended up at Cool UK, studying for NVQs in English and maths.
At Wellington, Grace proves most comfortable in the classroom. Just before lunchtime, we sit through a GCSE English lesson. There is a large interactive whiteboard showing an excerpt from the film adaptation of The Great Gatsby. The screen is filled with glittering flapper dresses and dancing girls and popping champagne corks. It is hard to think of anything that could be further removed from Grace's daily life. After a while, the teacher asks the class to write a descriptive passage inspired by the film.
Grace smoothes out a piece of blank A4 in front of her and writes her name in green ink with extraordinary care on the top left-hand corner. She decides the dresses look "sparkly like Christmas fairy lights". The teacher nods approvingly. "It's a very different lesson to the ones I had before," she confides. "It's very unusual because, at my old school, it was all tests and exams. We didn't do nothing like this. This is more chatty, and you get the chance to watch the film. We didn't have boards like this. We had blackboards and chalk."
The girl sitting next to her turns round and introduces herself as Alexandra. She used to go to a state school but came to Wellington on a golfing scholarship. The two of them start chatting about Burnley, where Alexandra's best friend lives.
"Are you going to come to Wellington?" Alexandra asks.
Grace smiles and shakes her head. "No. I'm just here for a visit."
Chris has been asked to write a short paragraph about the last time he can remember feeling truly proud. He sits at a desk, brow furrowed, pen in hand. Fifteen minutes later, he hands over his short essay. When I ask him what it is about, he grins, lolling back in the plastic classroom chair.
"I was 13 and I was playing basketball for the school. It was 30 seconds from the end and I had the ball and everyone was shouting: 'Shoot, shoot!' I just took it and scored." I tell him it sounds like a film and he looks genuinely pleased. "It does, doesn't it?"
After reading the short essay, David James, the mild-mannered director of International Baccalaureate at Wellington, says that he thinks Chris has the potential to pass GCSEs in English and maths. He is keen to set up a long-term partnership with Wellington that would involve Chris getting some form of tuition.
I'm not sure that a teacher has ever paid Chris a compliment before because the effect is quite astonishing. From being a recalcitrant, superficially moody teenager, he becomes immediately engaged. His shoulders relax. "Really?" he asks, looking almost bashful. "Yes, really," says Dr James. "And I wouldn't say that if I didn't think it were true."
Later, while we are walking to an interschool rugby match on one of the college's playing fields, Chris tells me that, "You need to have a good teacher. If you have someone dull and boring who says: 'Three eights are whatever' then you don't listen to them. But if you have a teacher who is really interactive, it's more fun for some reason.
"My old school was different from this one because they [the pupils] would have talked through lessons. Here they get it all done in the lesson and then they talk afterwards."
At the rugby match, it is bitterly cold and muddy underfoot. The Wellington team, despite spirited chanting from their supporters, are losing. Some of the pupils' parents have turned up to cheer them on. A bright red Ferrari is parked ostentatiously by the edge of the pitch. A woman in a matching fur hat and coat is walking a large dog around the school grounds.
Chris, Donna and Grace decide to slope off to the school tuck shop for crisps and chocolate bars. "I think they're exhausted," says Steph. "They need some time on their own."
I can see the three of them walking into the distance as the cheers of the rugby crowd recede behind them. They look like a huddled-together group of misfits in their sweatshirts and jeans, refusing to wear coats in spite of the temperature, unrepentantly themselves in the midst of this unfamiliar environment. For a moment, they seem very young and very alone.
But perhaps the most heartening realisation is that whatever their obvious differences or disadvantages, the children themselves find that they have more in common than what sets them apart. Several mobile numbers have already been exchanged and the Wellington pupils are very keen to make the return trip to Burnley.
"Everyone thought we were going to have different interests because our lives were so far apart," says Wellington student Frankie Paterson. "But deep down we were talking at night about film and music that we all have in common. The girls all liked chick flicks like Love Actually. We can have a discussion about it even if we're from different backgrounds."
Chris echoes the sentiment: "Everybody is just dead nice. There was nothing to be scared of. They are proper good people."
And it is true, that after a single day, you start to notice the beginnings of tentative friendships and shaky alliances poking up like fresh shoots among the thickets of mistrust and wariness. You can sense the transforming power of opportunity and the considerable effect that a teacher's genuine engagement can have on a child's self-esteem. But it is the moments that are only glimpsed by the rest of us - the whispered classroom confidences; the stifled laughter over a private joke; the indefinable sense of camaraderie forged in spite of difference - that prove the most potent.
• This article was amended on Sunday 11 January 2009. In this article, we stated that Chris Uthman had been expelled from Chorlton High, Manchester. We should clarify that he has not been permanently excluded; his "Cool UK" place was arranged by Chorlton High. This has been corrected.
