alt-j: A private jet, a Mercury Prize and Latitude 2015 headliners

alt-J have, finally, arrived. How do we know? Because that's their private plane (uh-huh, an Alt-Jet) parked at the local airport.

It seems that, in summer 2015, the enigmatic trio with the rarefied and kaleidoscopic math-folk palette – Mercury Music Prize winners for their 2012 debut An Awesome Wave – are rock'n'roll A-listers.

In a season of heavy and high-end touring commitments, bespoke aviation is the only way this band of allegedly cerebral, ascetic and notoriously nerdy graduates can make some of their bookings. Fulfilling a Glastonbury commitment last month had to be expedited by alt-J taking their own plane from France to Bristol. On the face of it, it's as likely as the Libertines opting to bicycle from T in the Park to Reading/Leeds. In lycra.

"It is crazy," sighs singer/guitarist Joe Newman, notably discomfited at the seeming extravagance. Antediluvian rock swagger is not something that sits well with him or bandmates Gus Unger-Hamilton (keyboards/vocals) and Thom Green (drums). "But it's 'cheap' because we're making money from the shows, and it's the only way we can make some of the shows."

"I do sometimes wonder if," adds Unger-Hamilton, "when they booked the shows, they thought, 'ah well, it doesn't matter about routing, they can just get a private jet…' If they had routed the tour more sensibly we wouldn't need private jets," he muses with impeccable Mr Logic diction and, ah, logic. "We heard that Aerosmith had it for their last tour," notes the tall, lean Cambridgeshire native whose inventive harmonies betray a cathedral chorister background.

"I was licking my fingers and poking in the seat lining, looking for crumbs of coke," jokes Southampton-raised Newman with deadpan humour. Alt-J may be a lot more entertaining and party-loving company than their reputation suggests, but that they're not that road weary and desperate. Not yet anyway.

It's 10 days before their Glastonbury appearance and a month before Latitude. The surprisingly physically imposing alt-J threesome are in Prague, chuffing fags backstage a couple of hours before showtime. Formed at Leeds University in 2007, they're touring the world in support of acclaimed, funked-up (okay, slightly) second album, This Is All Yours. Tonight, 4,000 people have gathered in a park by the side of the Vltava river to hear a band that seem as stoutly British as a mud-dy festival.

Yet this capacious turnout in the Czech capital is no local aberration. Alt-J are packing them in all over the planet. Since the start of the year they've sold out, among myriad other venues, Moscow's Crocus City Hall (capacity: 7,500), Brisbane's Riverstage (9,500) and New York's Madison Square Garden (18,000), not to mention London's O2 (20,000). When I saw them at the Coachella festival in April, they were an ear-poppingly entertaining – and surprisingly heavy – prelude to bill-toppers the Weeknd and Jack White. The response from the hopped-up, sun-dazed Californian hordes was ecstatic.

Their music's wide appeal, reasons Newman, 27, is about "having this interesting mix of something leftfield, but also this intrinsically accessible vibe to it as well."

With particular reference to America, Unger-Hamilton, 25, thinks that alt-J are perceived as "cooler and exotic because we're British. We used to joke that our American audiences were comprised of 50 per cent girls who were into alt-J, and 50 per cent lads who do like our music but are also there to try and get off with girls!" he laughs. "I think there's some truth in that."

Alt-J are, then, seasoned, worldly-wise performers. To entertain themselves (when not minesweeping for showbiz sherbert at 20,000 feet) they've embraced the touring lifestyle. Albeit with typically quirky intra-band bantz.

They talk of "Roadie Friday" (Unger-Hamilton: "A show night when the next day is a day off") and "Safety Burgers" (Newman: "If you're about to take a long-haul flight, and you don't trust the food, you have a burger before you get on, so you're able to refuse the in-flight meal.") And rather than befriending groupies or wrecking dressing rooms, alt-J and their road crew have invented a backstage game that they seem to play compulsively. "Throwy" is essentially a combination of donkey and ballet, it involves the throwing and catching of a small bottle of water, but with dynamic, rhythmic moves. Sounds boring, right? I played it with alt-J for an hour. Time flew by.

This month, the group go one louder and one further: they will headline a UK festival for the first time when they play Latitude. Not that they're letting their ascent to top-of-the-bill status change their approach to how they, as musicians, perform. Ask if they've invested in a bigger show production, and Unger-Hamilton replies that an increased lighting budget now involves "not being lit directly ourselves – we prefer to be lit from the side and the backs, so we make it look like we're just parts of an overall visual show."

"I won't be walking around, grabbing hands and taking selfies during the bridge of a song," says the so-called frontman, a smile playing on his lips. "It is really off-putting if you're aware that people can see you," frowns the mellow but heavily tattooed Green, 29, who's from Harrogate.

But, in fact, alt-J's light-under-a-bushel approach only makes them a more thrilling live act, as serial Latitude-goers will attest. They played the festival's Lake Stage two years ago. They then returned a year later, at the fag end of the same intensive tour, to headline the 6 Music Stage.

"When we came offstage in 2013," recalls Unger-Hamilton, "the organisers sent this really nice letter to our dressing room: 'You now hold the record for the biggest crowds at both those stages'. Which was really lovely."

"We were buzzing after the [2013] show," nods Newman, "but it was amazing to see festival promoters who were equally excited. Often at festivals they're literally pushing you off the stage… But we were sharing that moment together. That was when we really bonded with Latitude, I think."

So, alt-J are returning to Suffolk's Sunrise Coast as old friends of the festival, and a sense that they've progressed through the ranks. Yet with a brace of other global festival commitments this summer, they're equally savvy about the limitations of al fresco crowds' ardour. "We always say that at festivals you don't have a captive audience," says Newman, downing a pre-gig Czech beer. "They can just leave when they want – because they know that something else is happening elsewhere."

"And I have to remind myself onstage not to take it really personally when people walk away halfway through the set," chips in Unger-Hamilton. "I've done it myself! Watched a few songs, thought, 'that was really great, now let's get some noodles…' Not everyoen who doesn't stay for the whole thing thinks we're shit."

So how, then, will alt-J be doing their level best to maintain the interest of the main stage masses? Promise a ride in that private jet? Encourage a mass Latitude game of Throwy? Drag on Miley Cyrus, famously sampled in "Hunger of the Pine", the first track released from This Is All Yours? The threesome collectively wrinkle their noses at any such suggestions.

"They were trying to convince us to get Miley for Coachella," admits the keyboard player. "But we've never really gone in for having other musicians onstage and all that stuff…"

But lest that sounds a bit like "doing a Kanye", alt-J have one final suggestion. One that should appeal to Latitude's foodie-loving quotient.

"OK," accedes Unger-Hamilton, "we'll get Hugh Fearnley-Whittingstall onstage with us to butcher and roast a pig."

You heard it here first.

alt-J headline the Obelisk Arena at Latitude festival in Suffolk on Friday 17 July atitudefestival.com)