There was the stage invasion in Philadelphia that continued long after the gig had finished. Then there was the show in Brussels in a tiny, sweaty room, where the crowd were close enough to touch. And the three-hour performance at the Tate Modern in London, where a group of people got naked. It's a truism for any band with onstage chemistry, but to really understand the appeal of Factory Floor, you need to see them live. And if you've seen them play, you've probably got a story to tell.

Gabe Gurnsey, Nik Colk Void and Dominic Butler craft body music in the truest sense. Their propulsive rhythms create a kind of thrilling electric current, like live cables swinging from poles during a storm. It's at once organic and machine-like, controlled yet unhinged, instinctive yet deeply considered. On stage, Gurnsey hunches over his drums, part human metronome, part caged animal, while Void manipulates her voice, guitar and machines with focused elegance. Between them, Butler studiously plays his synths, communicating with his band mates through glances to his left and right. "I always feel like when we play live, there's something... I can't really describe it, but something happens, the lid comes off and everything explodes," Butler says.

All three cite the show at the Tate Modern last summer as their favourite gig—or, as they put it, "The one where people got naked." Playing for three hours with psychedelic visuals and the space's unique acoustics, their performance—which they treated like a rehearsal—slowly built to a point where people started taking their clothes off. "Out of the corner of my eye I saw these people, dancing naked, and it was fucking great," Gurnsey says.

Recreating the charged atmosphere of their gigs was one of the hurdles that confronted the band as they recorded their debut full-length. Two years in the making, the album has been produced entirely in the band's live-in warehouse space in Seven Sisters, an unfashionable corner of North London. "It's hard to recreate the live atmosphere in the studio because you don't have the audience to respond to, you don't have the nerves of the show, things that bring out a reaction," Butler explains. "But there was something else that happened in the studio, which was a different kind of thing, a different kind of energy."

That energy is something they captured on well-received EPs for labels like Optimo Music (which included their breakthrough track "Real Love") and Blast First Petite. DFA, which has already released two Factory Floor singles, will release their album. Though the New York label is a mixed bag stylistically, its dance-punk roots make it a good match. The label's 2010 reissue of Peter Gordon & The Love Of Life Orchestra is perhaps the closest link in its discography to Factory Floor—a framed poster of Gordon's short-lived disco project with Colette, Justine & The Victorian Punks hangs in the band's kitchen. Inside the warehouse, the trio's influences are all round them. A Throbbing Gristle poster is on another wall, and a worn Cabaret Voltaire LP pokes out from a small vinyl collection. There's a recording space, three bedrooms and a giant analogue mixing desk that was once used by the Eurhythmics. It's here I met the band. Gurnsey dabbed out cigarettes into an ashtray on the kitchen table, while the three of them reflected on the recording sessions that led to the album.

"We were writing, rehearsing and recording at the same time. We'd start something and we'd be scrambling to get all the cables to plug in to record it. It all got pretty mad," says Gurnsey, who stresses that the band's live-in studio space was the only way for them to record. "The time scale in which we work is a little more expanded than most bands," he says. "It was really important for us to be playing together to establish the foundations of the tracks, to try to get some chemistry. It definitely worked. You can feel the intensity on the record."

Part of the magic of Factory Floor's music is its use of repetition, and the gradual evolution of loops. The studio sessions left the band with long, unedited slabs of audio, and editing a 45-minute clip into a seven-minute track was no easy task. "I was hearing these things over and over again," Butler explains, "and it was like, 'Fuck, I've got no perspective on this anymore.' So we spent some time away from each track, and came back to it with fresh eyes and ears. That was very valuable."

It's a sentiment shared by the other two: "The repetitiveness of it can blow your mind a little bit," says Void.

"Eventually it just became this kind of pulse," Gurnsey adds. "But we have to play for a number of times for it to get to that point, where we're all locked in."

Simplicity was key during the recording process, though often it was forced rather than planned. "We had to go through a lot of stupid, complicated shit to get back to the most basic elements of what we do," Gurnsey says. "We spent a bit of time learning that that's how it needed to be done." Eventually they began to de-clutter their recordings, stripping them back to all but the most essential parts.

"I think a lot of people work like that, don't they?" says Butler. "They put everything on the table, and start taking things away until they find a shape that they're happy with. It's that creative way of refining something."

Further limitations—like a lack of direct power lines into their recording equipment and a tight budget—created some "nice restrictions," according to Void. Their minimalist approach is evident on the album's opening track, "Turn It Up," which eases into life with a bare-bones beat, and continues throughout the whole LP.

It's obvious that the band members share an obsession with sound. They've spent hours, days, sometimes months, tweaking and refining every sound on the album. "Tiny little things would make a massive difference to the track, like the subtlety of a drum hit," Void says. "So it was really fragile in that way, but at the same time it was pretty full-on. It was a contradiction. Everything we do is a contradiction."

Though they're used sparingly, Void's vocals are an integral part of the Factory Floor sound, and on the album they smudge the edges of tracks, sometimes discernible, sometimes a blur. "I would play about with my vocals for hours, manipulating and layering them, just playing with them until I was happy," she says. "I mean, there's hardly any verse on the album, there's not a lot of vocals there, but it took a lot of work to get me saying one word and getting it sounding how I wanted it to sound."

The band sent the record to LA producer Timothy Q. Wiles to be mixed down, and it's clear that handing over their work to a man they'd never met was not an easy decision. "It was a big gamble," admits Gurnsey. "It's a different art. His ears must be just fucking great." Though the band had previously mixed down their own tracks, Butler says Wiles "gave the album a real technical precision."

A curatorial residency at London's ICA ran in parallel with the album's recording process. This saw them collaborate with Hannah Sawtell, Peter Gordon and Mute Records mainstay Simon Fisher Turner. Butler says the ICA experience fed back into the album: "There were moments when we were really out of our comfort zone, but in a really good way. It brought out the playfulness of Factory Floor, and I think that's evident in the album."

The trio say the highlight was the improvised performance with Gordon last September. "We had to make a space for Peter's sound, so instead of just blasting it we had to be a bit more respectful and listen to each other and it was quite good to do that once in a while, I think," says Void.

"I was shitting myself before I went on stage," says Gurnsey, in awe of Gordon's technical prowess. "I mean, some of the intricate drum programming stuff he did with Arthur Russell, he had a very specific drum sound that's impossible to get nowadays."

And just as Factory Floor's live performances and collaborations fed into the album, the album will feed back into their live shows. "The songs, they're just points of ideas," says Butler. "And when you play live, you start with these motifs and they develop in a kind of improvisation... well, somewhere between improvisation and something a bit more structured. Depending on where we're playing and the response we get, it can go in all sorts of different ways. I'm really looking forward to seeing what we do with it."

The band tells me they've already begun working on a second album. "We've got a few ideas that we haven't used yet. Some of the things we worked on relentlessly and thought, it's time to put this track away, and maybe we'll revisit it in a couple of years. We had to just, sort of, have a full stop at the end of this project," says Void. "I don't think we're going to do it here. This place"—she looks around at the space they've called home for the past two years—"is going to be knocked down soon anyway."