It's a beautiful spring morning in Brooklyn, and The National's guitarist Aaron Dessner is unlocking the studio in the garden of his house. Once, he reckons, most of the houses on his street had stables at the back; he added his studio to the streetscape some years ago. It's a while since a horse was billeted round these parts.

The band used Dessner's space to record much of their 2010 album, High Violet , and to work on ideas for their new album, Trouble Will Find Me . Dessner uses it as his base for a growing portfolio of production work, which has included recordings with, among others, Sharon Van Etten and Local Natives. On the wall, whiteboards scrawled with track listings are testament to a busy schedule.

Right now Dessner's focus is firmly on The National, the band of Cincinnatians who came together in Brooklyn in 1999. Trouble Will Find Me arrives at an interesting time for the band.

Thanks to High Violet , The National became an overnight success after five albums. The bestselling work of their career, High Violet increased their fan base and saw them start to play bigger rooms. The songs remained the same – dishevelled, subtle, elegant, downcast, bruised accounts of love and loss, topped and tailed by Matt Berninger's distinctive grace note of a baritone – but the reaction was hugely amplified.

Dessner uses a great line to describe the songs of The National. You could also use it to sum up the band’s modus operandi: “Our songs sneak up on you.” He knows they are prime candidates for the least likely band to find on the fringes of the mainstream.

“We’ve always been surprised by any commercial success we get. We’ve done everything ourselves from an early stage. We’ve never benefited from any buzz, but we have somehow snuck into the mainstream. It’s a weird place. You find yourself making these decisions about how to market the record, which venues to play, balance the venues you want to play with the demand.

"The success of High Violet was much more than we ever anticipated. That was a little odd at times and made for some strange experiences, such as moving up to play arenas and hockey stadiums, or playing to no one in a field at Oxegen because we were put up against Beyoncé. We were surprised to find that we could make the move and not have to sacrifice the visceral aspect of the show, but it takes a lot of work. At this point we have a family around us fighting for us and caring for us."

The National's trajectory has been sustained by a strong connection with their fans and a live show capable of fireworks. "Ireland is a good example of that," says Dessner about their bond with their fans. "We really cherish our experience and audience there, because they've actually fuelled us. I remember back in Whelan's in 2005 the audience singing along, and it was one of the first times it ever happened. It created so much adrenaline to see how people were connecting with our songs. As you grow, you have to figure out how to keep that connection.

"We're a band who have an audience all around the world, and we want to play to all of them, so we can't do three or four Brixton Academys or Olympias in a row any more. I mean, there's no reason, strategically, why we went off and did the Other Voices TV show, for example, after playing those shows in the Olympia. But . . . we wanted to do it because our Irish friends told us it was cool. So we went, and it was."

Dessner and the band are also aware that their live show is another trump card. “The live show is pretty powerful. It’s obvious that the songs mean something to people, and you feel that. I know it sounds cheesy or corny, but it’s what pushes us on. It’s easy to forget when you’re in the vortex of recording an album that these songs will ultimately and hopefully take on new lives when people hear them and interpret them.”

They have found that the power to make decisions and demands tends to shift to the band as their audience grows. "During High Violet , we were still at a level where promoters could force us to do things," says Dessner. "Now I think we've graduated from that – we don't feel scared any more of saying, 'No, we're not doing that, we're doing this.' "

That Rolling Stones line about being born in a crossfire hurricane comes to mind when Dessner talks about recording the new album. “We lived in this barn upstate for six weeks. It was really nice for us to go away like that; it was like being at camp. The first night, though, a tornado came through. We were all set up, microphones and all, and you could see this tornado approaching, ripping up trees, and it knocked the power out for a week.

“We resorted to strumming guitars by candelight and playing drums with pencils, which we’d never done. Eventually, we went to another studio across in the Catskills until the power came back on. A few weeks later Hurricane Sandy hit.” Dessner pauses. “Yeah, it was eventful.”

Untroubled affair
Inauspicious start aside, Trouble was a largely untroubled affair. Dessner talks about the band being in good creative fettle on the back of High Violet and having only minor disagreements. "We have got to a point where the tension becomes exasperation; not at each other but the process. There were moments when you just wanted to bang your head off the wall.

"Before, there were some really bad moments where the band could have broken up. Everyone could have splintered off if we had wanted to. But during the High Violet tour there was a real cameraderie which had been there for years. I suppose we've all worked through the dark periods we had during the Boxer and Alligator years and came out the other side.

“At the level we’re at, it’s much more comfortable and the fog had cleared. There are bonds which go deeper than any one decision over a song.”

After more than a decade The National are comfortable in their skin. “When we started we were all obsessed with indie rock, especially Guided By Voices, Pavement and the Pixies , bands with interesting artistic careers, and labels such as Touch and Go, and Matador,” says Dessner.

“We really admired them because they seemed truly independent and in control. That was what we aspired to. We had no interest in popularity or radio play or any of that. We still don’t, and the band is not about that. Even the songs we write which are immediate aren’t really that immediate. But that’s the approach we like.”

Trouble Will Find Me is out on Friday. The National play Live at the Marquee, Cork, on June 28th; Odyssey, Belfast, on November 9th; and the O2, Dublin, on November 10th