Lost soul: Aidan Gillen is taking on an existential crisis in the spiky Mister John

Aidan Gillen is sitting in a first-floor suite of a grand old Edinburgh hotel. Overlooking the city's castle, the room comes with an impressively stocked honesty bar – pour your own drinks, pay later. Gillen is intrigued by the arrangement. "Do you have to pay for soda water?" he muses. "It's on the house, surely?" Deciding against testing this theory, he proceeds to offer an anecdote about an acquaintance who once took a thirsty group to an honesty bar, pretending to be a guest. "Then he passed out."

The Irish actor was once dubbed "dangerous" by Harold Pinter, after the late playwright saw him in a Broadway production of his work The Caretaker; and his best-known characters have certainly been brashly flamboyant – the predatory advertising exec Stuart in Queer as Folk, the hungry young mayor Tommy Carcetti in The Wire. But Gillen doesn't look the sort to indulge in such raucous behaviour in real life. In fact, judging from previous interviews, "diffident" might be a better choice of word to describe Gillen. Most profiles paint him out to be painfully reserved – "an heroically uncomfortable array of twitches and leers", said one writer – though that seems a mite unfair.

Today, there is no twitching, no leering, no facial ticks at all for that matter. But adjusting to the demands of fame, he admits, has not been easy – stretching back to 1999 and Queer as Folk. "People would come up to you and call you by your character name. I'd be like, 'Fuck! This is how it works.'" At first, he hated it.

Over time, as the roles changed, so did the name-calling – and his attitude towards it. In Ireland, where he lives with his wife and family, people shout "John Boy" at him, after the Dublin gang leader he plays in the Irish show Love/Hate. "I have no issues being called a character name now," he admits. "I quite like it."

It fits with a desire to hide behind his characters, which may account for why he considers himself only "vaguely recognisable" – and why, the day after our interview, he's able to stroll the streets of Scotland without hiding behind sunglasses. He's in town to support Mister John, arriving for the drama's premiere at the Edin-burgh International Film Festival (though apparently he took some persuading to do interviews, believing nobody would want to talk to him).

If he's a head-turner, it's more for his looks than his public persona. Now 45, and with those baby-blues as bright as arc lamps, there's something boyish about him, a quality undimmed by his dark hair greying round the edges.

This sex-symbol status flowed from Queer as Folk, the first of several landmark shows Gillen has slipped into. Russell T Davies' frank depiction of life in Manchester's gay scene saw the Irish Catholic Gillen indulge in explicit sex – although he never caught the flak he was expecting. While that was ground-breaking, Baltimore drugs-drama The Wire redefined the way we thought about television, unfolding in novelistic detail. Typically of Gillen, he insists on taking little credit for its success. When he arrived for the third season, "It was on the map, but it wasn't massive. I think it was Season Four that people really noticed it." He attributes that "largely" to the quartet of school kids who dominated that part of the show. "People really latched on to that."

Game of Thrones gave Gillen the third touchstone on his CV – playing the scheming Petyr "Littlefinger" Baelish. Unlike The Wire, which became the box-set to own after its fifth season ended in 2008, this quasi-medieval fantasy has escalated in popularity from the get-go. "It's one of the biggest TV series in the world now," he nods. "But again, it's a huge ensemble thing; you're never carrying too much of that weight. Nobody is. I'm in and out of it."

In danger of sounding falsely modest, Gillen does acknowledge, on being pressed, that being in three such important shows is, "not just luck. I'll go after stuff; I think I can read a script and say, 'This is good'; and if it's not good, then I'm not going to go after it. Filtering it that way, whatever you end up in is going to be good. You don't always get it right, but those things [that don't work] don't show up so much."

In the case of Game of Thrones, Gillen certainly did his homework, having read all the books in A Song of Fire and Ice, the series by George RR Martin that form the basis of the show. So can he give us an informed explanation as to why it's been so successful? "Tits. Beheadings. Wizards," he jokes, before adding: "Big story, real characters rooted in reality with magic and sorcery on the periphery but family, war, death, power… all these things, they're universal themes." Not one to over-analyse, he simply seems happy to be involved. "I guess that's where I make my living right now."

His involvement also allows Gillen a career in the sort of films he wants to make – low-budget British gems such as two movies he made for the under-appreciated director Jamie Thraves: twentysomething drama The Low Down (2000), playing the restless Frank, and the gritty Treacle Jr (2010), which saw him take the title role, an effusive, eternal optimist. "I've probably had my best time acting – or not acting, or trying to not act – on things like The Low Down or Treacle Jr," he says. "I'm happiest doing things like that. Not just because they're lead roles, but because there's more freedom in them."

Mister John, a sparse but spiky drama, feels like a distant cousin to those films. Gillen plays Gerry Devine, who arrives in Singapore after his brother dies, to attend to his affairs. Leaving behind his rocky family life, he picks up the threads of his sibling's existence – from wearing his clothes to frequenting the bar he owned. "Gerry's enjoying being lost," says Gillen. "It seems far preferable to his life back home in London." It's a theme that resonated with Gillen. "Personally, I quite like getting lost like that and not knowing what's going on."

There was plenty of time for that, it seems. "I hadn't been to Singapore before," he says. "I hadn't been to the East at all. Anywhere further than Turkey, which isn't really the East, although it's getting there. I felt Singapore was quite Western, actually, more than I was expecting, and had an air of Los Angeles about it."

Directed by Christine Molloy and Joe Lawlor, who made the acclaimed art-house film Helen, Mister John is not without its lighter moments – not least a bizarre scene in which Gerry is bitten by a snake and the venom causes an involuntary erection. Gerry is forced to take a painful trip to an acupuncturist, where needles are stuck into his manhood; thankfully, Gillen didn't go Method for the role. "She wouldn't do it," he smirks, referring to the actress in the scene. "She wasn't a real acupuncturist. I said, 'What about the one in my hand?' She couldn't get it out!"

Gillen has a penchant for the twisted – when he made Dominic Savage's 2009 drama Freefall, one memorable scene saw him clinch a multi-billion-pound deal and then disappear to the toilet for a bout of celebratory self-relief.

Clearly, though, he leaves all his demons at work: he has been married to Olivia O'Flanagan since 2001 (they met years ago, in Dublin), they have two children, 15-year-old daughter Berry and 12-year-old son Joe, and they live on the west coast of Ireland, preferring tranquillity to the buzz of the city.

For one who seems to craves domesticity, is it difficult to be away from the wife and kids so often? "It's worked out fine – I'm never away for that long," he says, explaining that "for 50 per cent of the time" he's at home. "Even when we were doing The Wire, they were coming over a lot or I was going back to London. Once you establish a bit of trust with the producers and they know you're going to come back… I think maybe some actors miss a plane. But I don't!"

Born in Drumcondra, Dublin, as Aidan Murphy (later adopting his mother's maiden name for Equity reasons), Gillen is the youngest of six, the son of a nurse and an architect. His early days were spent making "fake movies in the back garden" with his siblings. They didn't even use a video camera; it was all pretend – with Gillen cameraman, director and star. Not that he was the only one in the family with artistic ambitions. His sister Fionnuala Murphy is an actress, best known for her appearance in Stephen Frears' take on Roddy Doyle's The Snapper, while brother John Paul is a television writer and playwright.

When a neighbour decided to try out for Dublin's Project Arts Centre, Gillen went along, partly for the social aspects, and soon graduated from bit-parts to A Midsummer Night's Dream's Bottom. Three years later, when he was 19, he gained his first film role, "gate-crashing the set, basically" of Jack Clayton's adaptation of Brian Moore's The Lonely Passion of Judith Hearne, earning the princely sum of £700 – a lot of money back then – for playing "Youth in Liquor Store".

His first real breakthrough came in Antonia Bird's 1993 Bafta-winning television drama Safe, playing the homeless youth Gypo. And, four years later, a small role in Mojo, Jez Butterworth's film adaptation of his own 1950s-set play about Soho gangsters, proved a turning point. He played, with some brio, the psychotic Baby. "This trail of villains, these darker roles, started around there. The stuff I'd done before that was quite the opposite."

Mojo saw him befriend co-star Harold Pinter – and it was the playwright who later recommended him to director David Jones for The Caretaker. While Gillen has frequently returned to the theatre – from Shakespeare's The Tempest to David Mamet's American Buffalo – Jones's 2003 production was a catalyst: despite playing opposite the more experienced Patrick Stewart and Kyle MacLachlan, Gillen was the one walking away with the plaudits and a Tony nomination. ("Of the three," wrote The New York Times, "only Mr Gillen is fluent in the language of ambiguity that is the currency of Pinterland.") When the play opened, the late Bob Colesberry, an executive producer on The Wire, saw Gillen roar across the stage – and his role as Tommy Carcetti was secured.

More recently, Gillen made his first concession to major-league Hollywood, playing a CIA operative in Christopher Nolan's conclusion to his Batman trilogy, The Dark Knight Rises. "That was me gigging for a few days, for fun. It was interesting…" He breaks into an uncomfortable laugh, before quickly extolling the virtues of Nolan. Understandably, he says that if he had to choose between a blockbuster bit-part and a low-budget lead, the latter would always win out. "I wouldn't be so quick to take on one scene in a film like that any more, I think. " He stops himself before he says anything else. "Ah, forget it."

Gillen is fully aware that he needs to maintain his "name" to help generate financing for micro-budget projects – and he's been able to spend the past year shooting Brit-flicks Still and Calvary in between bouts of Game of Thrones. But keeping himself castable doesn't mean casting about for any opportunity. "I try to keep my integrity," he says. "I don't want to be in Hello! or on Celebrity Big Brother." In fact, the only reason he did the Batman film was for his kids. "To get some cred with them. They might not be too bothered with some of the stuff I've done over the years, but Batman… that's another matter."

‘Mister John’ (15) opens on 27 September