Wolf Alice are one of those rare bands that seem to stand for something bigger than themselves. They write proper indie anthems – scuzzy, snotty blasts of attitude that dance with the ghosts of alt.pop past without feeling slavishly in their debt. Singer Ellie Rowsell is their secret weapon. She’s a drop-dead, fringe-in-her-face enigma in the vein of Kim Gordon, Kathleen Hanna or Shirley Manson – a pin-up for sensitive boys down the back and a role model for the empowered girls up the front. In an age when music is plastic and disposable, mere fodder for your playlist, Wolf Alice give you something to believe in.

“We can’t ask for anything else in the world,” says bassist Theo Ellis, contemplating 18 months of mind-bending over-achievement that have seen the north Londoners graduate from obscure support slots to prominent billing at Electric Picnic. “It can be be quite overwhelming and you do have to be conscious about keeping your sanity. At the same time, how can we complain? Every week we get to go to a different festival in a different city. It’s amazing.”

But success has a downside in that, as we speak, Wolf Alice are figuring out how to do it all over again. Debut album My Love Is Cool came out a year ago and now Rowsell and co are getting to grips with a follow-up. It’s true, says Ellis. Your second LP really is the one that challenges you – tests the limits of what you considered possible. They’re deep in the trenches now, figuring out what comes next.

“It’s that old cliche, isn’t it? You put your whole life into making your first record. Then, suddenly, your daily experience is all about touring and being away and on stage. And that’s such a familiar refrain from bands. But we’re excited about doing it all over again. It’s early days yet. We’re trying to take our time, give ourselves space so that we don’t rush into things.”

There was a fair degree of buzz preceding My Love Is Cool. Nevertheless, expectations are considerably higher second time around – a situation with which the quartet are wrestling on an ongoing basis.

“You can’t let it permeate your consciousness – or the music will be shit,” says Ellis. “Lately we’ve had to come to terms with the fact that life has changed for us all. It is strange – this is our thing now. We’ve had to build a new way of living.”

“One thing in our favour is that we have absolute freedom. We are going into the studio and taking the songs to their natural conclusion. We’re not trying to change things radically – to sound like a chill wave version of ourselves. Our management and label are great. They know people want an authentic representation of what we are. Audiences can tell if something is contrived.”

Rowsell has become the predictable locus of attention – something she finds both flattering and off-putting. She is still uncomfortable in the spotlight and, try as she might, cannot make herself smile to order. “Being well-known, or sort of well-known, is weird,” she said recently. “It makes you self-conscious. It also makes you watch everything you say in a public situation, especially in interviews, or between songs on stage.”

“I like to think we’re pretty jokey people, self-deprecating – and we can be quite moronic, too – but we’ve had to learn to be careful in how we present ourselves, just in case. People are very quick to take offence at the slightest thing, aren’t they – and then blog about it.”

She has also struggled with the pressure to be glamorous a burden heaped exclusively female musicians.

“I don’t really care about fashion, I don’t always wear make-up, I don’t scrutinise outfits for hours,” she told the Telegraph. “But I’m starting to think about it, which is a bit of a shame. The boys can wear what they want in photo shoots but I get asked to wear the latest collection from blah-de-blah or they want to do my make-up and it takes an hour. I treat it as part of the job but if you were insecure, it would be a headf**k.”

Rowsell started Wolf Alice as a solo project in 2010. Keen for collaborators, and with her father helping out, she went online to look for potential bandmates. Eventually she stumbled upon footage of Joff Oddie, a trainee teacher and aspiring guitarist. At his suggestion in 2012 they recruited drummer Joel Amey and bassist Ellis.

“She sent over her demos and I remember thinking there was obviously something very good here,” Oddie would recall. “I liked her voice. It is one of those things – it’s hard to put your finger on. She had it. We listened to a lot of folk-pop at that time, Johnny Flynn and Laura Marling – that freak folk stuff that was knocking around back then. It’s very different to what we listen to now.”

From nowhere to headliners in just a few years, it’s little wonder that Wolf Alice have often had to pause to pinch themeless. On the festival circuit, they have shared bills with artists such as Beck, Neil Young and Dave Grohl of Foo Fighters. Hanging out with icons back stage is an education – surreal and illuminating at the same time.

“That has happened a few times – it has always been quite weird,” says Ellis. “You’re getting to know them or having a beer or whatever, and it’s strange. At the same time you are in a professional environment so there is a sense you are equals. There is a reluctance sometimes to meet people you have admiration of – in case they re assholes. ”

Electric Picnic is on the horizon and they can’t wait. “We always love playing Dublin. We supported the 1975 in the Olympia two years ago and it was our favourite gig of the tour. And we’ll never forget seeing Beck at Electric Picnic in 2014. It was amazing – hands down one of the best festival performances I’ve ever seen. We’re looking forward to coming back.”

See Wolf Alice at Electric Picnic