For all the time Haim spent in the UK at the start of their career, you might be forgiven for thinking the three sisters were actually British.

Of course, once you hear them talk you realise they’re Los Angeles through and through.

Their adventures on British soil started in May 2012 when they performed at Brighton’s The Great Escape festival. It was the first time Este, 27, Danielle, 24, and Alana, 21, had played outside California, and almost as soon as the final chord of their set had been struck they were being hailed as the next big thing.

Their first release, the Forever EP, hinted at an impossibly bright future for the trio who used to drive around LA listening to a mix of their parents’  Fleetwood Mac and Motown records and California’s finest AOR and pop radio stations.

In a way, they seemed almost too good to be true. Their own songs, somehow new and classic at the same time, the fact they’re sisters, their good looks and attitude were the obvious draws. Yet look a little harder and there’s more going on.

Middle sister Danielle had toured the world as part of Jenny Lewis’s band. When she wasn’t drumming for the former Rilo Kiley singer, she was playing guitar with Julian Casablancas of The Strokes’ touring band.

Este, meanwhile, had gained a degree in ethnomusicology from the prestigious UCLA, while Alana, barely out of her teens at the time, was passing time as a babysitter and spending every spare moment practising.

Before 2012 was out, they’d toured Britain three or four times, did so again earlier this year and are about to head out on the road once again. There are bigger shows booked for March, most of which are already sold out.

Despite their hectic schedule, Este still hasn’t managed to learn to sleep on the road, confessing to suffering from chronic insomnia.

“I’ve tried everything,” she says. “Everything apart from proper sleeping pills. I don’t want to take those, though, because I know I’ll go full Elvis, put on a load of weight and start wearing jumpsuits.”

They have been supporting French band Phoenix on their European tour, something Alana, a die-hard fan, can’t quite get over.

“I grew up listening to Phoenix, and now I’ve been hanging out with them and watch them every night from the side of the stage, which is kind of crazy,” she says.

As is often the case, bands break in the UK first and watchful eyes in America take note. As soon as Haim had scored a Top 20 single over here, not to mention clinched the BBC’s Sound Of 2013 poll, they were back home, doing very similar things in the US.

“Finishing the year touring in Britain just makes so much sense because it feels like we owe it all so far to you guys,” says Alana. “I love the UK so much. I’ve never ever wanted to leave LA before, but then I went to London and it’s the only other place I’ve ever been to that feels like home.

“One minute I was working as a nanny and it felt like I’d never ever leave the States. The next thing I hear our song on the radio and the flights were booked.”

Their debut album, Days Are Gone, came out in September. Initially it was intended to be released sooner but due to the band’s self-imposed standards – Danielle’s rumoured to be especially particular – it wasn’t ready.

Eventually, almost 18 months after their first single – an eternity as new bands and modern schedules go – the album arrived. It duly went to No.1, selling just under 50,000 copies in its first week and beating Justin Timberlake to the top spot.

Haim met the Prime Minister on The Andrew Marr Show
Haim met the Prime Minister on The Andrew Marr Show

“Worked out OK, didn’t it?” says Este. “There were delays, but when it was finally released it was just about as close to how we wanted it to be as it could’ve been. We were all so happy.

“Then we heard the release date we’d chosen was the same day as a whole bunch of other records, one of which being Justin Timberlake’s album. That was it, we thought, our chances of being No.1 were gone, which was fine, but we did it. And we went to No.6 in the US, which is incredible, too.”

Alana adds: “It was frustrating at the time, but when I look back, I’m not scarred by the long nights and ripping my hair out in the studio. There were times when I thought we should’ve scrapped everything and started again, but now I think that talk is hilarious. The record’s exactly what I always hoped it would be.”

For a record that was worked on for so long, one of Days Are Gone’s most admirable traits is how breezy it all sounds. So often, the more a band edits their work – and especially a band that works with numerous producers as HAIM did – the more character they chip away.

It’s testament to the sisters’ songwriting and conviction that it all manages to still sound so natural. Singles Forever, Falling, Don’t Save Me and The Wire are natural standouts, but they don’t overshadow new songs like If I Could Change Your Mind, Running If You Call My Name and the title track, an ode to growing up and leaving their parents’ home behind, a common theme on the album.

“This whole year or so has felt like a highlight,” says Alana, “but playing Glastonbury sticks out as the real ‘pinch me’ moment. I’d always dreamed of playing there, and we performed on three different stages, one of which was with Primal Scream on the Pyramid Stage. I mean, are you kidding me? It feels like I’m lying when I tell people.”

“We’ve always had this idea of what we wanted to sound like,” says Este. “It’s always been so clear to us, and it takes the strength of all three of us to do it.

‘‘It takes time, trial and error, and we really have put the effort in, and have had support from people around us.

“The hardest thing has definitely been getting to where we wanted to be, and now we’re almost there. That’s the beauty of being three sisters. I’d be lying if I said we weren’t intimidating when we’re together.”

* Haim play Birmingham Institute tonight (December 5). They return to the Midlands next year for a gig at Nottingham’s Rock City on March 4.