Gabriel Prokofiev runs a clubnight in London. DJs play between live sets, the bar is busy, people mingle. Then, a string quartet walks on to set up their music stands. They tune up and wait for a hushed silence before beginning to play. This is a night of classical music.

Prokofiev is a composer, just like his famous Russian grandfather, but he also runs the Nonclassical, the classical music clubnight. His own music is frequently performed there, along with that of many other contemporary composers. As a music student at York he was constantly frustrated by the divide between the world of classical music and the rest of his life. He tells me that his reason for starting the whole enterprise was simply that he wanted his friends to hear his music.

Why should classical music belong only in concert halls? It certainly didn’t originate there. Indeed, why can’t it be heard in the same venues as popular music? Nonclassical challenges assumptions about what classical music can be. Gabriel is very keen for the night to become "a regular feature of London nightlife". If it takes off, classical music could be seeing an entirely new audience.

I’ve been to Nonclassical several times, and was also invited by Gabriel to curate. Several of the musicians I normally play with refused to take part: "Why should someone be allowed to chat to their friends and drink when they should be listening to the subtle nuances I have been practicing for six hours a day!", they protested. I would argue that if six hours’ practice a day is really worth it, then you should be able to persuade someone to listen to you rather than to buy another beer.

When I raised this problem with Gabriel, he explained that the point of Nonclassical is not that the audience is noisy, but that they could be: "the atmosphere you get when a whole room of people listen silently even though you know they could be drinking or talking is incredible", he says. He finds the etiquette of the concert hall unhealthy: "You have no idea what audiences are really thinking, and this really has allowed a lot of crap trends to continue in concert hall music." Nonclassical makes the interaction between performers and audiences more real, and therefore more risky.

In his Bethnal Green studio Gabriel shows me his current work, which includes remixing a Beethoven symphony for John Axelrod. He visited France to record samples in a rehearsal, and had a great time having the choir do whatever he wanted, experimenting with different languages, ranges and sounds. But he insists that he "doesn’t want to just be remixing old classics," and the Nonclassical website describes the clubnight as "possibly a new genre of music". When I question him more closely about this, he laughs apologetically and says: "that quote is a bit old, maybe we should have it taken down. But if I had to, I guess I’d describe the genre as immediate, punchy, and rhythmic – not typically academic."

It is true that contemporary classical music is often seen as ‘academic’ – complicated, atonal and boring – and classical composers today are faced with disinterest. Gabriel takes a very different approach to music. He says that "ideas from electronica and dance music – looping, and production techniques" have influenced his pieces through his work as DJ and producer.

Indeed, one only needs to hear his string quartets or the Concerto for Turntables and Orchestra that he wrote for DJ Yoda in 2006 to feel these influences. While composers such as Vaughan Williams used folk melodies in their music, Gabriel treats electronica and hip hop as the ‘folk music’ of today. His work is tuneful and exciting, rhythmic and immediate – and still modern. "Most composers nowadays aren’t creative enough," he says. "The problem with writing a piece without having the experience of listening to it fully is that you divorce it from reality, when the whole power of music lies in distorting time and perception."

I’ve been to other similar nights in London which try to make the music ‘friendly’. One of these is This Isn't for You, curated by Matt Fretton at King’s Place. It all feels so patronising: they casually lay out bean bags, turn on ‘mood lighting’, and give you beers in plastic glasses. For some reason – maybe because it’s so disorganised, grimy, badly presented and chaotic – Nonclassical feels real. Gabriel’s clubnight is redefining ‘classical’ for a new venue, and a new generation.