It is surely a national outrage that Ofsted inspectors, who judge schools on “performance”, “curriculum” and “leadership”, can’t also spare a tickbox for “incredibly talented recent alumni who have just recorded an album so extraordinary it can only be described as soul music for skeletons”. For if such a category existed, the four 19-year-olds who make up the new band The xx might be able to save their alma mater from being deemed "inadequate". As it is, their South London comprehensive, Elliott School, has recently been placed under Ofsted’s rather Orwellian-sounding “special measures”, and its governors replaced.

Yet its accomplished former pupils are not a one-off. Their music may be highly original, and hailed by many critics as the greatest debut of the year, but they are merely the latest in a long line of such innovative musos to graduate from the troubled school.

Burial, nominated for the Mercury Music Prize last year, went there under his real name, Will Bevan, as did Kieran Hebden of Four Tet, half of Hot Chip, Adem and a Maccabee or two. Their music ranges between electronic, folk and guitar; united by quality and creativity rather than one particular sound. (Older alumni include the 1950s star Matt Monro, “the singing bus driver”, and Pierce Brosnan, though one might not add his vocal skills on Mamma Mia! to the school’s list of achievements). While the BRIT School, also in South London, is overtly focused on the performing arts, nurturing Adele, Amy Winehouse, Katie Melua and some of the Kooks, this comprehensive seems to have produced equally talented artists without any of the showbiz backing.

So why would such a good school close? “The thing is, it had the same amazing head teacher for about 25 years,” says Oliver Sim, who co-fronts The xx with his lifelong best friend, Romy Madley Croft. Indeed, that headmaster, Victor Burgess, was appointed OBE for services to education in 2002, his school recognised as one of only ten with “outstanding” leadership in a government study. His pupils then showed so much interest in school reunions that they won the Friends Reunited award for Britain’s Friendliest School in 2004. “But after he left they started going through a lot of head teachers,” Sim continues. “The amazing thing about it had always been the freedom: no real uniform, quite progressive. But the new head started introducing uniforms, the right kind of shoes, and big fences, with electronic gates.” Madley Croft adds: “It already looked like a council estate prison anyway, so when you’ve got to buzz in with a swipecard ... We were happy to leave when we did.” It wasn’t all freedom though — she once cut up her uniform a bit and her head of year rang up her father “and said, ‘She looks like she’s going to a rock concert’. My dad just laughed”.

Yet they can see how the school shaped their music. Along with their bandmates Baria Qureshi and Jamie Smith — the latter of whom also produced the band’s eponymous album — these quietly intense young people make slow, sparse tunes. A downbeat landscape of synthesised beats, where the lonely twangs of a guitar build into layered melodies, and the male- female duo of Sim and Madley Croft’s voices wrap around each other like breathy snakes. As the blog Pinglewood.com put it, “They are a band who understand what Debussy meant about music being the space between the notes.” While their peers jump around on stage in ever more frantic attempts to be rock’n’roll, The xx stand stock still. It is remarkable to watch people so young yet so at peace with the stillness at the heart of things — until you find out that they studied minimalism for music GCSE.

“I was trying to work out where my guitar sound comes from and I recently realised it’s from Philip Glass,” says Madley Croft. “I remember sitting in a practice room at school, playing the same riff again and again, with slight changes, because that’s what we had listened to. There were the practical lessons and the written ones, where we talked about minimalism and the blues.”

Yet it was also the sense of space in the school itself — which itself was “weirdly massive”, according to Sim. Various alumni tell me that the school’s musical success is not so much from the teaching as the lack of it; the freedom to use rooms and equipment and put on your own shows. Madley Croft and Sim were even allowed to take Wednesday afternoons off to rehearse their music.

After they left they signed to the Young Turks imprint of XL Recordings, home to the White Stripes and Radiohead. The pair then had a surreal period of working during the day at Uniqlo and Costa Coffee, then writing their songs separately in their bedrooms in the middle of the night, sending parts to each other over the internet, adding to what the other had done. “I have to credit my dad for this, too,” says Madley Croft, “because he had trusted me after I left school to spend a whole summer staying up all night in my bedroom with my guitar and my laptop in bed. It gets to 2am, and then 4am, and nobody is online any more and you are left on your own — that’s the writing time. Everything seems to come out at that point. But you have to push yourself to get to there — it makes you a bit funny.” She kept her singing talent a secret, as did Sim, who also remained strangely private about his work, “always conscious that my mum might be eavesdropping at the door”. (He has now allowed his mum to come and see the band play live — she liked them so much that she burst into tears.) Their musical predecessor Hebden says that he would be sad to see the school close, having had “an amazing time there”. He went back recently for a teacher’s leaving party and was depressed to see the state that the school was in. “Elliott should be one of the great comprehensive schools in London and it’s disturbing that this has been allowed to happen.”

Still, there is one consolation in all this, as he points out. “At least if Elliott needs to put on a benefit concert to save the school we could get a great line-up together.”

They’d be the hottest tickets in town.

The xx’s debut album, xx, is out now.

They play Leeds and Reading Festival and are on tour in the UK until October 7; www.myspace.com/thexx.

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