Conor Curley slowly, carefully pours himself a Guinness upstairs in King Tut's Wah Wah Hut and reflects on his home city of Dublin. 'Some of the best art is written about places when they're in certain times of flux', he explains. 'Dublin's in that place right now. It's loosening its grip on the things that made it really good. But as you see that happening it's beautiful as well.'

Fontaines DC, the five-piece Irish indie band with which Curley plays guitar, have just released their debut album Dogrel. It follows a slow and steady couple of years in which they've relentlessly toured and charmed audiences and dropped a handful of attention-grabbing singles. At present they're one of the most exciting guitar bands in Europe, their deserved ascent showing no sign of slowing. The band excels in the big picture that Curley describes: portrayals of fury and injustice sit side-by-side with earnest and tender evocations. This is a band for whom the poetry is everything.

The band met at BIMM, a music college in Dublin. Original members Curley, bassist Conor Deegan III, drummer Tom Coll and frontman Grian Chatten (guitarist Carlos O'Connell joined later) would talk about music, words and their adopted city – only Chatten is a native – over pints after class. They were inspired by the path followed by their compatriots Girl Band, beloved noise-rock surrealists and trailblazers for the now positively flourishing Irish music scene. They shared a love of The Pogues. They bonded over Yeats, Kavanagh and – of course – James Joyce, whose 1914 short story collection Dubliners is a huge influence on Dogrel. 'That collection is so special to us,' Curley says, solemnly. 'We'd like to think of our album as a collection the way Dubliners is.'

While the circumstances are different a century on from Joyce's writing, the ideas are similar: the pursuit of identity and the search for meaning and purpose are everywhere in Dogrel. 'We have a real romantic sense of this beautiful old city with so much history', Curley says, 'but at the same time – in the real sense … I used to work service jobs and you see people are being pushed out. Big companies are coming in, taking all this land and driving the rent so high.' Curley tells of a friend who commutes to Dublin for work – from Glasgow. The frightening thing is that this, in the year of our Lord 2019, is a wholly unsurprising option.

When it comes to looking to their environment for inspiration, the band are in good company. Detroit punks Protomartyr ('fuckin' great band', says Curley) reflect on the rapidly changing city of Detroit to riveting effect. Curley himself was impressed with Goat Girl's self-titled debut album from 2018; a sprawling and often grim portrayal of life in modern London.

And so Fontaines DC ended up working with Goat Girl producer Dan Carey on Dogrel. 'Me and Grian (Chatten, the band's singer) went over to meet him and he blew us away with the way he talks about music,' Curley explains. 'He's a deep thinker, a mad scientist. Doing the first album with him will make all of our albums a lot better.' Carey was keen to capture the energy of the band's live show and – despite some initial resistance – convinced the band to work in his own tiny studio, performing live in one room. 'He was right', Curley says, effusive in his praise of Carey, who he calls 'a really good friend of ours now, and a good mentor', adding: 'The way we did it really helped, we recorded songs in blocks of three, one after another, playing them live. We'd go into 'Boys In The Better Land' after doing two other songs, just like a live show.'

The band are open minded as to the musical direction they might take next. Tonight they finish their set with a new song; a confident move, considering the last song on the setlist is arguably their signature track – 'Big'. Curley talks pre-show of a dub influence – it's palpable. 'A lot of the songs are different genre-wise on Dogrel', Curley says. 'I'd say, a lot broader than a lot of albums that get released these days. Because we've done so many singles it gave us the opportunity to do that. I feel bands now, if they release an album, they're gonna do one definite thing as well as they can, and be very strict to genre and influence. You cut yourself off. You go to your second album and people want a similar sorta thing. With us, it feels we've no walls now. It seems like a lot of the ideas we want to do we can put into the Fontaines set up. If I wanted to explore heavier, industrial sounds … if we weren't like that I'd have to do that somewhere else. Whereas we feel like we can do anything. If the five of us play on it, it'll sound like us.'

If there's one thing Curley has no interest in exploring as a songwriter, it's Britain's exit from the European Union. 'I'm sick of people in Ireland being too obsessed with what England is doing', he says, explaining that his only worries surround his family based back in the border county of Monaghan. 'It worries me a little but as a stance I just turn my back to it. I tried to follow it and my head was spinning, it was doing me no good, it's not an inspiring thing. I want to write things that are character-driven. People connect more so to genuine writing about certain characters' situations and how those principles are set. I don't want to write songs that are lists of demands – it's fuckin' bullshit. If it was me, man, and a singer was telling me all these things … fuck that'.

The band are keeping a frantic schedule throughout the summer; an American tour with label-mates Idles ('I really love what those lads are doing. I went to see them in Dublin a week ago, and I've never felt energy in the room like that.'), festival dates and finding time in-between to work on new songs. 'I'm the same as all of the lads,' Curley says, 'one thing I can't get out of my head is what we're gonna do next. Because it's really exciting.'

Dogrel is out now on Partisan Records. Fontaines DC play TRNSMT on Sat 13 Jul, tickets are available now.