Aidan Gillen is perched on an oversized sofa, head-to-toe in black save for brown boots and the two splashes of silver among his short dark curls. His face is pointedly handsome. The definitive word on his unblinking gaze comes in his best film, The Low Down, in which his co-star tells him: “You’ve got, um, quite starey eyes, haven’t you?”

Gillen isn’t accustomed to being the centre of attention. Even after taking a prominent role in Game of Thrones – as Littlefinger, the calculating brothel owner – the 47-year-old has refused to be defined by the pop-culture colossus. “I enjoy being part of that world,” he says in a voice scarcely louder than falling snow. “It’s a phenomenon, but I’m not slap-bang in the middle.” The same could be said of an earlier HBO show, The Wire, in which he played a Baltimore politician whose idealism took a bruising.

Now and then, he’ll turn up in something glossy – The Dark Knight Rises, or the latest Maze Runner film. But you would need to go all the way back to Channel 4’s Queer as Folk in 1999 to find him fully in the spotlight. That’s how he likes it: “If you can walk into a room where there are 20 people who don’t know what to expect from you, then you can pretend better.”

Over the coming weeks, he will be almost alone on stage, accompanied only by the pianist Feargal Murray, for a series of candlelit readings of James Joyce’s masterful short story The Dead. Set at a bustling party on the feast of the epiphany, the story sifts through the trifling worries of a professor who will, by the end of the night, have experienced an epiphany of his own.

The idea of the reading was sold to Gillen as “Jackanory for adults”. Yes, he’ll have the 16,000-word story in front of him on stage. “But it has a lot of dialogue. People talking at the same time. It’s full of characters and you have to inhabit them. You can’t just be stuck in a book.” His accent sees to it that “stuck” rhymes with “book”.

It isn’t far removed from reading a bedtime story to his kids, he says. “I suppose children usually haven’t paid. Maybe they should. They might pay more attention.” The idea amuses him; a smile flickers on his lips. “I think people who don’t know the story will be pleasantly surprised. They might come along expecting Finnegans Wake, but this is very accessible; it has more in common with Chekhov and Dickens.”

Like Joyce, Gillen also left his motherland, though his own departure wasn’t stormy, and he still has a home there. “I don’t know if I could’ve stayed and worked as an actor. Actors in Ireland tended to come from other professions. Brendan Gleeson and Gabriel Byrne had both been teachers. But I was ready to go when I left school. I didn’t want to spend five years doing something else.” He had never been outside Ireland when he hopped on a boat at the age of 18. “I grew up in Dublin. But I grew up in London, too. It was here that I found out who I was and what I was going to do.”

Stage and film work followed, but Gillen’s arrival was announced most emphatically in 1993 with Safe, Antonia Bird’s BBC2 film about London’s homeless youngsters. He played Gypo, who could be wildly self-destructive and achingly tender, often in the same scene. “We shot it in three weeks. I had this feeling of elation. I never wanted to sleep. I probably didn’t, either.” His performance looks today like a statement of intent. “Well, I had the intent but no technique. I meant what I was doing. I just didn’t know how to do it.”

Gillen’s co-star, Kate Hardie, spent the entire shoot with him. “Aidan’s really tricky because sometimes he doesn’t say much,” she tells me. “He might just growl at you and you’re thinking: ‘You’re quite peculiar.’ It took me a long time to work out that he’s very shy. But he was always a brilliant, surprising person. Once we were in a bar at four in the morning and some guy came up and wanted a fight. I was terrified, but Aidan immediately stood up and said to him: ‘Do you wanna dance?’ And he started dancing with this guy! It was one of the best things I’d ever seen.”

In the years since Safe, there has been no shortage of work, some of the sparkiest of it on stage – in the original production of Jez Butterworth’s Mojo, or on Broadway in Pinter’s The Caretaker (after which Ben Brantley in the New York Times said that Gillen gave off “the subliminal hum of an electric generator”). He has no compunction about being bells-and-whistles bonkers when it suits him: he was at his most inspired as a hammer-wielding cop-killer in the Jason Statham thriller Blitz. To prepare for that part, he made apocalyptic videos and tried to buy a hammer while in costume and in character. “They wouldn’t sell me one,” he says proudly. “That’s when I knew it was working.”

But it’s striking that he has rarely collaborated on film with a director of longstanding repute: no Loach, no Leigh, no Stephen Frears or Neil Jordan. My theory is that he wanted to remain footloose, to work with emerging, experimental talents, but he puts me straight. “They never asked!” he protests. “If Gus Van Sant or Paul Thomas Anderson were to offer me a part, of course I’d do it.”

His most fruitful collaboration has been with the British film-maker Jamie Thraves, with whom he has made three movies. In their first, The Low Down, he played an introverted, borderline-depressed dreamer. “That character was just me in someone else’s jacket,” he grins. Thraves recalls the audition: “Aidan said his lines so quietly that my producers and I had to lean forward to hear him. You couldn’t take your eyes off him.

“It was so powerful. He has that classic quality that only the best actors have: you’re not sure what he’s thinking. He’s very unpredictable.” The pair reunited in 2010 on the bittersweet comedy Treacle Jr, and are now putting the finishing touches to Pickups, in which Gillen, who also co-wrote the script, plays himself: a method actor who keeps being recognised as “that man off the TV” in public.

“It’s a version of me,” he explains when I ask if the film expresses any ambivalence about fame. “There’s a sense of ‘I hate it and I’d miss it too’. It’s not a moany-whiny thing. I love my life and what I get to do. But it’s a weird job.” What makes him do it? “You get to experience all the most exciting things from a whole lifetime condensed into two hours. You get to live all these lives and it feels real – it’s the same chemicals inside you as if these things were really happening to you. It’s almost like an illness, you know?”

• The Dead is at the Sam Wanamaker Playhouse at Shakespeare’s Globe, London SE1, 14-28 December.