It's 8.30am, and in an 18th-century Palladian villa in Richmond Park, London, 25 children are saying their prayers. "God be in my head and in my understanding," they recite, heads bowed. "God be in my eyes and in my looking…"

At first sight, they resemble any other bunch of 11-year-olds. Look again, though, and they don't. For a start, they all share the same physical proportions. Long necks, trim shoulders, neatly made upper bodies poised on long legs. They're preternaturally neat, and glow with health and purpose. They look happy, and perhaps they have reason to be so, for they know themselves to be special. These are the youngest students of White Lodge, the Royal Ballet Lower School. Every one of them hopes to become a professional ballet dancer. They are, says White Lodge principal Diane van Schoor, "the clay".

White Lodge is a boarding school. It was established in 1955 by Ninette de Valois, founder of the Royal Ballet, to provide dancers for the company. Entry is by audition and each year about 1,000 11-year-olds compete for two dozen places, making it one of the most selective educational establishments in Britain. Students stay at White Lodge for five years and, at 16, audition for the Royal Ballet Upper School in Covent Garden, where they spend a further three years, graduating as professional dancers at 18 or 19. For most, the dream is a place in the Royal Ballet itself.

Over the years, however, the odds against home-grown British students fulfilling this ambition have steadily lengthened. Statistically, only around a quarter of those first-year White Lodge students are likely even to graduate from the Upper School, let alone be considered for a place in the company. The Royal Ballet and its schools comprise the nation's flagship classical dance establishment, so why are the odds so comprehensively stacked against British children? Jane Hackett, a former director of the English National Ballet School and the Central School of Ballet, now co-director of creative learning for Sadler's Wells Theatre, is concerned by the figures. "It's inexplicable, when you look at the amount of money invested in British ballet, that such a very small percentage of British dancers are graduating and progressing through companies."

Pitch perfect: boys enjoy a kickabout during their lunchbreak. White Lodge has been a boarding school since 1955 Photograph: Hugo Glendinning for the Observer

To make sense of this issue you have to separate the often contradictory strands of the Royal Ballet's organisational culture. Excellence figures strongly in the mission statement and the Royal schools spare no effort in bringing potentially talented pupils into their orbit through outreach programmes. There's an assumption that ballet goes hand-in-hand with privilege – in fact the students at White Lodge come from every imaginable background. The fees exceed £30,000 per annum, but no successful candidate is ever turned away. Instead, families are means tested and, in more than 80% of cases, are supported by government grants.

The parents of Sam Lee, from Dagenham, knew next to nothing about ballet when Sam was introduced to dance by the Royal Ballet's Primary Steps scheme, which sends accredited teachers into schools. Now Sam's at White Lodge. "You see dancers like Carlos Acosta and it's inspiring. The training's hard, but I tell myself don't give up. Carry on!" Sam's attitude suggests that he may have the right stuff to make it. But he's going to need every ounce of that determination.

It's 9am, and teacher Nicola Katrak, a former Royal Ballet dancer, is putting the Year 7 girls through their paces in one of the White Lodge studios. Their upper backs don't yet have the ironed-out flatness of the older students, their legs are not yet fully turned out from the hip and their feet not yet fully arched, but the evolution is under way. And as they move forward as one into arabesque – standing on one leg with the other lifted high behind – it's as if they leave their children's bodies behind. Ballet is about physics, about advanced co-ordination and muscle control, but there's a metaphysical element, too. You don't perform the arabesque, you become the arabesque. It's about transformation.

These girls are here because, even at 11, most of them instinctively understand this. As they progress through the school they will be drawn deeper and deeper into ballet's abstract dimension. This will compound their sense of vocation, bond them to their fellow students, and set them subtly apart from the world outside classical dance. The idyllic surroundings, the intense friendships, the sense of insidership – all these are remembered with great affection by former White Lodgers. But for those who do not make the grade, the sense of loss can be acute. One girl who was recently asked to leave the school was described as "absolutely devastated. Traumatised."

In the next-door studio, Hope Keelan is teaching the Year 7 boys. Standing bare-legged at the barre in leotards and shorts, they look much more vulnerable than the girls, and lack their self-containment. One moment they're puffed up with achievement, the next they look quite lost. Homesickness is a big issue and both Keelan and van Schoor confirm that boys seem to take it hardest. At the beginning of the school term, says Keelan, she has sometimes conducted classes to the sound of "sniffing and sobbing".

"I was homesick at first," says Misha, a London boy named after the Russian ballet star Mikhail Baryshnikov. "But you have to go forward. We talk to each other, talk about home. And now I love it so much here I couldn't give it up." Ellie, a freckled Liverpudlian, agrees. "You realise what a nice place you're in. It's really homely."

Today’s lesson: boys finish with a handshake with teacher David Yow. Photograph: Hugo Glendinning for the Observer

And it is. The dormitories are particularly welcoming, with each girl's area individualised with toys, family photos and posters of favourite ballerinas. The boys' quarters are comfortably informal, too; former Royal Ballet star Sergei Polunin described his time at White Lodge as "like being in Harry Potter". But the obstacles these children will face are formidable. They will be subject to term-by-term appraisal and at the end of each year some will be "assessed out", or asked to leave. Perhaps they have failed to reach the expected technical standard, or their bodies have developed in ways that do not comply with the school's increasingly narrow physical ideal. Short-backed and long-legged, in the Russian mould, this is very different from the longer-backed "old" Royal Ballet look and there is a certain irony in the fact that many of the school's ex-company teachers, were they to present themselves today with the bodies they had as teenagers, might well not fit the mould.

Additionally, the British White Lodgers have to compete for their places with increasing numbers of students brought in from abroad, a process many find stressful and demoralising. For Claire Calvert, a talented young Royal Ballet dancer who went through White Lodge and the Upper School, it was "very difficult" when, each year, yet another cadre of overseas students arrived. Some of her friends were worn down by the ceaseless competition. "It's so mentally draining. There are girls who say: 'I just don't want to go on.'" And many didn't. Of the 19 girls who joined White Lodge with Calvert, she was the only one to make it into the company.

For one former teacher at the school, the system is fundamentally unfair. "The children who go into White Lodge are the most talented in the country. They prove their commitment by leaving their homes and their families, aged 11. If I was a parent of a child who'd made that kind of sacrifice and then been assessed out, I'd be pretty unhappy." In this teacher's view, echoed by many in the British ballet world, the onus should be on the school to make the best dance artists it can of the children it selects. The "difficult" students, experienced teachers say, are often the most creative, and freedom from the fear of being assessed out would powerfully enhance that creativity. As Hackett says: "The approach, if someone's struggling, should not be 'we've got to get rid of this dancer,' but 'what can I do to make him better?'"

Principal Diane von Schoor. Photograph: Hugo Glendinning for the Observer

Whatever its ethos, the place is Arcadian. In an airy studio shot through with shafts of spring sunlight, van Schoor is teaching the Year 11 girls. At the piano, a young man is playing Chopin. Not with the chugging rhythms of the day-in, day-out ballet accompanist, but beautifully and sadly, as if it matters to him. The girls, now 16, have acquired their working ballet bodies: pulled-up, long-muscled and racy. Along with the Year 11 boys, they will soon face "final auditions" for the Upper School. Only about half will make it, and they know it. There is an undercurrent of acute, sublimated anxiety. "Jeté en avant, jeté en arrière…" sings out van Schoor, demonstrating the flickering jumps with an insouciance that none of her students can quite match. She makes them repeat the exercise, showing how an oppositional torsion of the upper body, known as épaulement, brings the otherwise academic sequence to life. And then watching them, shakes her head. "You all look as if you're going to Sainsbury's. And I've got news for you. The sale's over."

The White Lodge candidates who make it into the Upper School will be joined by students from other UK ballet schools and from overseas. They will live in accommodation owned by the school – there are boys' flats and girls' flats – and will do their own shopping, cooking and laundry. As at White Lodge, part of the syllabus is given over to conventional academic studies. All students leave with three A levels and a BTEC in dance, scoring well above the national average. "Some find A levels very difficult," says Royal Ballet School academic head Charles Runacres, who has taught at Cambridge University and Eton. "But the concentration and the desire to do well does transfer from ballet". Those who survive the three-year course can expect to graduate as professional dancers. Gailene Stock, director of the Royal Ballet School since 1999, prides herself on the fact that for the past five years, all her graduate-year students have won contracts with international ballet companies.

Ready to fly: final year students rehearsing for an audition. Photograph: Hugo Glendinning for the Observer

In one of the Upper School's spacious, purpose-built studios, a second-year girls' class is under way. The teacher is Anita Young, a former Royal Ballet soloist, and she is trying to get the girls, who are mostly 17 or 18, to think about expressiveness. "Listen to the music!" she keeps telling them. The girls are formidably technically assured, but they look tense, watching Young with large, nervous eyes. When they take balances they tend to gravitate backwards, as if fearful of commitment to the position. "Weight forward," Young implores. "You can always have a nose-job. You can't mend a broken back!"

"They're so lovely," Young sighs after the class. "And their legs go far higher than ours ever did. All this, though…" And here she strikes an attitude, the position pliant and alive, her arms framing her face with subtle épaulement. "All this is gone." But if her pupils go for eye-catching hyperextensions and "six-o'clock arabesques" rather than nuance and refinement, it's perhaps because they know that in an audition they have to grab a director's attention fast. In a mercilessly unforgiving milieu, their instincts are fine-tuned for survival.

Evie Ball rehearsing. Photograph: Hugo Glendinning for the Observer

Evie Ball, a smiling student from Liverpool who dreams of dancing the role of Manon with the Royal Ballet, went through White Lodge and now, at 19, is in her graduate year at the Upper School. She has loved her time at the school and made lifelong friends there, but has always been conscious of its Darwinian back-beat. "They started assessing us out in Year 9, when we were 13," says Ball. "And it kicked in that this was a competition. The final term at White Lodge was really nerve-racking; less than half of our class got through to the Upper School. And now, of those, there are just three boys and four girls left."

A substantial percentage of Upper School students are from overseas, either fee-paying or on scholarships. Many are recruited at international competitions or at Royal Ballet summer camps while in full-time training in their home countries, a practice one British ballet parent calls "absolute poaching". But according to Gailene Stock, searching out the most talented students worldwide is only sensible, given that ballet is a globalised business. Their presence in the school, Stock insists, inspires the home-grown students, and many ballet migrants, such as Alina Cojocaru (from Romania) and Marianela Nuñez (from Argentina, but now a British citizen), both of whom spent time at the Upper School, go on to become lustrous stars of the Royal Ballet.

It's a vexed issue. Cherry-picking gifted foreign students, processing them through the school and skimming off the crème de la crème for the company, certainly keeps the statistics looking good, and makes sense in market-economic terms. But it also makes for a company without much of an identity or unanimity of style. British dancers are often late developers. With time and care, as the history of the Royal Ballet has proved time and time again, they flower into artists of subtlety and sensitivity.

Melissa Hamilton, from Northern Ireland, was refused a place at the Royal Ballet School. She was taken in hand by a Russian teacher who saw her potential, and who patiently set about turning Hamilton into a ballerina. Eventually, the Royal Ballet accepted her and, earlier this month, the 23 year-old made an acclaimed debut as Juliet at Covent Garden. But how many Hamiltons never flower at all? How many drop out in their teens, their self-esteem in tatters, convinced they're failures?

Gailene Stock with Rouen the dog. Photograph: Hugo Glendinning for the Observer

Pretty much everyone in the Royal Ballet establishment admits that there's a crisis of confidence among their young British dancers. Gailene Stock, who is Australian, talks of her British students' "reserve". They tend, she says, "to stand back and admire". And this diffidence carries over into the company, where out of 29 Royal Ballet principal dancers and first soloists, only five are British-born and trained. British dancers still make up a majority in the company, but most languish in the lower ranks. No one in the establishment is prepared to make the connection between these dancers' lack of confidence and their schooling experience, but to many observers it's a clear case of cause and effect. "If you're operating from a basis of fear," says Hackett, "you can't hope to develop confidence, expressiveness or personality".

Part of the problem lies in the nature of the establishment itself. Management scientists talk of "the organisational dilemma". How do you reconcile the conflict between the needs and aspirations of an organisation and those of the individuals who make it up? No one at the Royal Ballet School is unconcerned with the pupils' wellbeing and, in many cases, the affection of staff and teachers for those in their care is palpable and touching. But the organisation is attempting to master two conflicting roles: as a national arts organisation with its roots in the community and as a globalised free-market player. These roles are in constant collision and the home-grown dancers are caught between them.

It doesn't have to be this way. Globalisation notwithstanding, the world's great classical dance companies – the Bolshoi Ballet, Mariinsky Ballet, Paris Opera Ballet, New York City Ballet and others – draw almost exclusively from their own schools and home-grown students and, in consequence, maintain an individuality of style and tradition which the Royal Ballet, for all the brilliance of its imported stars, has lost. Commercially speaking, you underestimate the appeal of local talent at your peril. Darcey Bussell was a wonderful dancer but British audiences loved her first and foremost because she was a home-girl, one of their own.

At White Lodge, where a new day is beginning, posters of Bussell still feature on the dormitory walls. Downstairs the Year 7s are saying their prayers. As well they might. Last year, two former White Lodgers out of an original cadre of 24 graduated from the Upper School into the Royal Ballet. This year the figure was zero.