The first time I saw Sheku Kanneh-Mason play, it was hard to tell where the cello ended and he began. It was May, and I had switched over, slightly late, to his performance in the BBC Young Musician final; rather than the sharp, four-note theme at the start of Shostakovich’s Cello Concerto No 1, I heard the high, lyrical repeated notes a couple of minutes in to the Russian composer’s 1959 masterpiece. The 17-year-old was leaning back slightly, rocking with the movement of his bow, his left hand dancing far up the cello’s fingerboard with no sign of strain. He powered through the rest of the music with some astonishingly emotive playing, his face contorted, biting his lip with the effort of memory and control. Once he came to the end, for a few seconds he looked shocked at what he had done – then he smiled.

A month later, I walk into a room at the Royal Academy of Music in Marylebone, London, and find Kanneh-Mason hunched over his instrument again. He is playing softly to himself as our photographer circles him. Though it has been a hectic four weeks since he won the Young Musician competition, the piece that secured his victory is still living in his fingertips.

The reaction to Kanneh-Mason’s ­triumph was almost universally positive. Not only is he the first black winner of the Young Musician award, he is also a rarity, in that he has achieved this while studying at a comprehensive school. Commentators have remarked on the startling maturity that shines through his interpretations of music. The raw emotion in the Shostakovich concerto – the grimly frenetic passages, the Russian melancholy, the ironic quotations from Stalin’s favourite song – all find an outlet in his playing. There are musicians with an entire career behind them who struggle with this aspect of performance.

When I sit down with him, I am suddenly conscious that he is only 17. The poise he has shown throughout his summer of sudden fame makes you forget that he isn’t even in his last year of school. He seems nervous and a little defiant (very teenage), although when I ask about his concerto he can’t help but grin. “It’s Shostakovich’s last battle against the Russian regime, and there are bits of anger, despair and loneliness – especially in the second movement,” he says. “I often think there are bits of sarcasm and humour in it, too, and places where he’s taking the mick, especially in the last movement.”

Kanneh-Mason is serious about music but there is no sense that he is a hothoused talent, cut off from the real world. “I play football quite a bit,” he says. He is also keen on schoolwork. The day after we met, he sat his maths AS-level exam (he is also taking physics and music). He attends the Trinity School in Nottingham, a Catholic comprehensive; it has been understanding about all the time out he has needed, he says. And he admits that he has become “a little bit” of a celebrity since the competition – teachers show clips of his performance in assembly and younger kids congratulate him in the corridor, which is clearly embarrassing.

Although the competition was the first time that Kanneh-Mason had performed as a soloist with a professional orchestra, he had been on television before. Last year, with his brother and four of his sisters, he featured on Britain’s Got Talent. After a minute or so of listening to the group’s playing, Simon Cowell’s face lit up in astonishment. They made it to the semi-final, where they performed a classical medley on a podium surrounded by billows of dry ice. “Bringing classical music to a wider audience than it normally gets was kind of our main goal,” he says. Indeed. When was the last time classical music got any airtime on ITV?

Sheku is the third eldest of the siblings in a family whose musical talent would put the von Trapps in the shade. Isata, the eldest at 19, is studying at the Royal Academy (she has a scholarship funded by Elton John) and was a Young Musician piano finalist in 2014. She accompanied Sheku in the early rounds of his competition. His brother, Braimah, a year older than Sheku, also took part in the 2014 Young Musician in a string quintet. The only child in the family who doesn’t have Grade 8 in at least two instruments is Mariatu, who is six. She has recently started learning the violin.

Growing up in a musical household has its benefits, Sheku says. Practising doesn’t feel like a chore because everyone is doing it all the time, even if it can get a bit crowded.

“I go in my bedroom, my brother goes in his bedroom, and then the girls fight over the pianos,” he says. There are three, apparently, but one is “rubbish”. Getting to the top demands sacrifices. Along with some of his siblings, he awakes at 4.30am on Saturdays to get to London to attend the Royal Academy’s junior school, and there are times when he can’t play football with his friends. “They’re cool with that. I think they all understand it’s hard work.”

His years spent travelling up and down the country for cello lessons have taught him a few tricks: he does his schoolwork on the train, when it’s impossible to practise.

Kanneh-Mason might be on the cusp of a professional career but he is also a millennial and prepares for performances by watching videos on YouTube. His role models as a cellist are Jacqueline du Pré and the Russian Mstislav Rostropovich (for whom Shostakovich wrote his cello concerto). He is also a big fan of Bob Marley and has been known to wear Marley T-shirts. Another influence is the British cellist Guy Johnston, who won the Young Musician competition in 2000 playing the same piece. A mentoring relationship has developed between them; after our interview, Sheku and his younger sister Jeneba went to rehearse for a chamber concert with Johnston.

Looking back on his own experience of the competition, Johnston advises caution. “The danger is that you get this amazing early burst of experience and opportunity . . . I think there’s a point at which you realise that it’s not a sprint, this whole business. It’s a marathon.” Being anointed by the BBC at such a young age can be a great burden of responsibility. “He’s got a very strong family,” Johnston says, “and a very wise head on his shoulders. I’m sure he’ll manage the inevitable complexities ahead.”

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Although the competition, which has run every two years since 1978, is most definitely presented as “highbrow”, it has more in common with Simon Cowell’s TV talent shows than many would like to concede. Winners and finalists usually go on to some kind of musical career. For the most part, they become orchestral players, or teachers. The few who become household names and enjoy international solo careers, with their face printed on album covers, are generally good-looking, too. Making it as a classical crossover artist is about more than skill: you’ve got to have the image to go with it.

Arguably there is even more pressure on Kanneh-Mason to succeed, because black faces in British classical music are so rare. He has already been signed up to appear in a BBC4 documentary titled Young, Gifted and Classical, to be broadcast in November, which will tackle “issues of diversity and access in classical music”; and he will doubtless be in demand for ensembles that are eager to prove their progressive credentials. Several of the Kanneh-Mason siblings are members of the Chineke! Orchestra, the first in Europe to be made up entirely of black and minority-ethnic musicians. Writing in the Guardian, the double bassist Chi-chi Nwanoku, who founded Chineke!, described Sheku’s Young Musician win as a huge boost for all those who want to see greater diversity in the field.

Kanneh-Mason is fairly laid back about his new status as a political symbol. “It doesn’t bother me,” he shrugs. “If a lot of people see a young black guy from a comprehensive school playing classical music, they’ll think that’s quite cool. My job is to just do a good performance.” When I ask about his background, he says simply, referring to his mother, who is of mixed race: “I’m Welsh.”

There is no doubt that classical music is a white, middle-class preserve, but data on the full extent of the problem is hard to come by. A 2014 study of five leading conservatoires in the UK found that 8 per cent of students and just 2 per cent of staff were black or from an ethnic minority.

Kanneh-Mason’s parents, Stuart and Kadiatu, are not professional musicians and they have spoken repeatedly about the challenges they have faced in trying to give their children the instruments and tuition they need. Stuart is a business manager and Kadiatu a university lecturer who gave up work after Sheku was born. His family is originally from Antigua, hers from Sierra Leone and Wales. Speaking to the Daily Mail after her son’s win, she said: “Every penny of our money goes on music. We haven’t decorated for years . . . The tiles are coming off the roof. We never buy new clothes. I do the girls’ hair myself because it’s too expensive to take them to a salon. Our car is a wreck.”

All of the siblings have won scholarships and they play high-quality violins and cellos, on loan from a retired plumber in Barnsley called Frank White, who started making instruments in 2002. Sheku hopes to follow his elder brother and sister to a conservatoire after his A-levels.

Later, as I watch him play with Guy Johnston, listening to the way they throw the melodies in a Vivaldi concerto back at each other to create a vivid, beautiful texture, it is easy to see why Kanneh-Mason puts up with all the scrutiny and pressure. His brow is furrowed in concentration, but there is joy in his eyes.

Sheku Kanneh-Mason performs with the Chineke! Orchestra at the Royal Festival Hall, London SE1, on 4 September. Details: southbankcentre.co.uk