"Who the fuck is Laurent Garnier?" Outfit, perhaps the least physically imposing band in the capital, have got beef with one of France's best-loved DJs. Garnier played the band's excellent single 'Two Islands' on a recent edition of his podcast and, in a rare misstep, the DJ disliked the track so much that he cut it off halfway through. Garnier described the song's drizzle-soaked tones as "sugary pop" – which, as inaccurate descriptions go, is pretty tough to beat.

'Two Islands' is, however, a near-perfect encapsulation of Outfit. It is defined by its internal contradictions: at once ambiguous and immediate, pensive and hopeful, danceable and full of melancholy, it is indicative of a band intensely comfortable with conflict.

But more than anything, 'Two Islands' feels like the sound of Liverpool – or, at least, of the quiet dockland tragedy that has become synonymous with the European Capital of Culture 2008. To many hailing from anywhere south of Watford, images of Liverpool tend to be conjured up in greyscale, heavy with roll-up smoke profundity. "It's a bit of ready-made imagery," says guitarist Nicholas Hunt as he sits with two of his bandmates in Lincoln's Inn Fields, London's lawyers' quarter.

Outfit left Liverpool eight months ago, having spent the preceding few years weaving themselves into the city's underground fabric. For a band whose identity appeared so tied up with their hometown, the move seems counterintuitive. But, as they point out, the sound of Outfit is not the sound of a specific city, but rather of generalised urban life. Their debut EP, Another Night's Dreams Reach Earth Again, was released mid last-month. It feels simultaneously concrete and corporeal, speaking of disoriented, conflicted urban inhabitants, and to their dislocation from the environment in which they find themselves. In its four tracks one can trace the topography of the contemporary city, its looming peaks and its deathly hinterlands. The record's breathy atmospherics are offset against brief, joyous conflagrations - the sounds of the subject trying to claim their space in an environment characterised by hostility.

That dislocation has become a lyrical preoccupation since the band arrived in London. "The songs have much more to do with displacement," says Andrew Hunt, frontman and brother of Nicholas. The band's line-up is completed by Thomas Gorton, Christopher Hutchinson and David Berger. Moving has had, Andrew continues, "a direct impact" on the music the five-piece are writing.

Nicholas agrees: "It's about scale. Having to shift your aspirations and the way you work. Having to be really flexible. I think it's a representation of a difficult time. A time when we're all knackered because we're trying to make it work while also making our lives work."

The band have left behind a small but enthusiastic scene in which they appear to have played a central, if playful role. "We've done a lot of stupid gigs," says Andrew. "Van Halentine's Day. That was a speed-dating event we organised on Valentine's Day. We publicised that David Lee Roth was making an appearance. The local news picked up on it, and some people from Manchester came to see David Lee Roth. And it was obviously just us. We did another gig in French accents. Oh, and Christmas Naivety, which was a nativity show." YouTube footage reportedly exists of the band being thrown out of a venue after dragging their friend offstage midway through a song called 'Ketamine Crucifix' ("He really wasn't a musician," says keys player Thomas Gorton). I suggest that the problem with the internet is that this incident will be forever archived, but Nicholas disagrees: "You can edit your past, but why pretend to be someone else? I was that guy in Norwich Unicorn."

Indeed, online space is as much of a fixation for Outfit as that of the city. Lyrically the band explore the intersection between the urban and the digital, constructing individuals whose identities are formed through antagonism with the city and with the internet. "It's fascinating that now everybody self-advertises and self-edits," Nicholas says. I'm interested in younger people, who've grown up with the internet more. The idea that you can edit other people's perceptions of you, or that you can have more control over other people's perceptions and over your identity is fascinating. It's so mediated. That gap between who you are and how you are perceived has always been there, but it's much more overt now. It would be really strange to grow up with an 'about me' built in."

Outfit's own online identity is an expertly constructed adjunct to their music. On one page of their website the same press shot is projected, wraith-like, onto a series of indeterminate domestic objects. On another the screen is entirely filled with clips of YouTube users, each delivering their monologue direct to camera. One is in a petting farm; another complains about her parents. In a third, a 'medium' talks about having sex with ghosts ("5,000 people worldwide claim to have had some sexual interaction with a ghost or spirit", apparently). Their YouTube favourites, meanwhile, suggest the exhaustive lists of artists made on the MySpace profiles of particularly conscientious music fans circa 2005. Arthur Russell and Japanese composer Toru Takemitsu sit next to Group Doueh, while elsewhere Bauhaus promos nestle close to clips of KONK on Andy Warhol's 15 Minutes.

There is a sense of scrapbooking; a feeling that the band are not just broadcasting their taste, but rather stitching together an extended audio-visual collage. They are clearly interested in more than 'just' the sounds of instruments. Instead, they seem drawn to music with a life outside the recording; music which comes with a compelling visual artefact, or which is presented in unusual ways. It is unsurprising, then, to find that Gorton has been listening to "Saharan cell-phone music. In certain parts of Africa they pass around music by Bluetooth. It's all really, really badly produced, but they have amazing, undeniable groove, despite the fact that they sound like ringtones."

Outfit are in the early stages of work on their debut long player, and are contemplating producers. "We're basically stockpiling songs," says Andrew. "It would be nice to work with someone else who understood where we're coming from. But by this point we have such a feeling of the direction and the production that we want, that we need someone who's willing to accept that. It's hard to ask someone to come onboard as a producer, because they're going to end up with being very protective."

In the meantime, though, the band have crafted one of the most exciting EPs of the year so far. Another Night's Dreams… is very much a record of its time. Contradictory and contentious, it's the sound of a very specific contemporary urban existence – and a compelling first move for a band already several steps ahead of many peers.

Outfit play at Field Day tomorrow, Saturday 2nd June, at London's Victoria Park.