“We all love telephone banking”, say Jack “Wandeck” Patterson and Grace Chatto from their Kilburn studio. Not the words you’d expect from one of the hottest up-and-coming bands around; but then Clean Bandit, who have “five to seven” Cambridge degrees between them, ranging from Russian to Architecture, are not the people you’d expect to go into making seriously cool electro-classical tunes.

All the members of the group – Grace, Jack, Ssegamic, Milan and Luke – studied at Jesus. Ssegamic, lead singer and vocals writer, was recently made the youngest-ever nominee at the global Institution of Chemical Engineers Awards, exhibited photography in Boston,and spent a month in Haiti researching the possible use of sugar-cane charcoal as an alternative fuel. "He gets around", Grace says in a thoughtful tone.

The band formed in 2008. Grace, the cellist, and Wandeck, who writes most of the music, went on a year abroad to Russia and found the band’s name in the English translation of a nickname given by Grace’s sister – “it actually translates more like, ‘ultimate bandit’”. Though they hate the word "fusion", Clean Bandit have somehow managed to create what they call "electronic chamber music" – electro merging seamlessly with the classical segments by Chatto’s eponymous quartet which predates the band. They haven’t been afraid to sample the greats, as track Mozart’s House shows, but Wandeck has recently begun to compose the string parts too, as in Telephone Banking. Even so, their new, as yet unnamed single, relies heavily on Mozart’s D Minor quartet. It doesn’t get more – and less – Cambridge than this. They’ve been described as“playful” by the Guardian and variously as “highbrow” and “dope” by the blogs, but how do they describe themselves?

“I don’t know about highbrow”, Chatto laughs. ‘When we started, we just wanted to make music we and everyone else could dance to, that was a bit different.”

So what can you expect at a Clean Bandit gig? Their low point so far was having the power cut out at Hay-on-Wye: an increasingly enraged band and crowd watched the sound engineer scurrying around for ten minutes, until Ssegamic began spontaneously singing and got the quartet playing. Meanwhile, Wandeck fought it out with the engineer – “until I realised I’d just kicked the plug out with my foot”, he laughs.

How does it go when they’re not accidentally sabotaging themselves? “We tend to do a couple of covers every time we play – Sunchyme by Dario G, and Stand by Me which is actually going to be on our EP”, says Grace. Ah yes, the coveted and elusive EP. Are they signed? For Clean Bandit, that would be too easy. They shunned Warner Brothers and Mercury for spending more time on their songs and releasing them on their own production label, Incredible Industries. What happens if they hit the big time? "It’s not complicated stuff", says Chatto. "We’re all into fun", says Wandeck; "there’s still quite a strong direction amongst the members; it’s quite hard to push stuff through".

They’ve now played at St John’s four years in a row, but otherwise the band has come far since Cambridge. They have just set up their own production company, cleanfilm.co, so they’ll continue to make their own videos, for themselves and other artists. Mozart's House is a Sledgehammer-esque whirl of stop-motion shots, whilst Telephone Banking features slower, more thoughtful clips and Japanese kids brandishing cellos. Since Telephone Banking, they’ve even been approached by Channel 4 to make something “fictional and hopefully interactive”.

Their website has the usual cryptic polygons that have come to signify hipster chic – except these make sounds when you run your mouse over them and are, Chatto says, a template for future instruments: “we’re going to make a diamond-shaped green cello and a small, round violin. In terms of the image, we don’t want people to think that we’re trying to be cool”. One wonders how long it takes before Clean Bandit realise they don’t have to.

You can watch Clean Bandit's Telephone Banking and other music videos here