There is an intriguing story told about Domhnall Gleeson: that he's such a self-critical perfectionist he thinks he's singlehandedly ruined every film he's been in. Oh no, that's a complete exaggeration, he says, between sips of a beer that he shouldn't technically be drinking. (He's due on set in a few days, to star alongside Julie Walters and Jim Broadbent in an adaptation of Colm Tóibín's Brooklyn. "But, you know," he says. "Fuck it.")

No, of course Gleeson doesn't think he's singlehandedly ruined every film he's starred in. Just most of them. "Yeah, I had a nasty surprise recently," he nods. "I watched a couple of films I was in and thought, 'Those are pretty close to what we wanted them to be. I feel actually weirdly OK with it all. I can still see flaws in what I'm doing, but I think I delivered. I think I improved the film with my presence.' And then I watched something else and I thought, 'I fucked everything up.' It was a total crash down. It was like, 'Oh no, I've done it again.'"

The notion that Gleeson has lurched from one disaster to another, ruining everything from the Coen brothers' remake of True Grit to Richard Curtis's romcom About Time, seems a pretty unique interpretation of his burgeoning career as a versatile character actor. In the last couple of years, he's gone from the romantic lead in About Time to Konstantin Levin in Tom Stoppard's adaptation of Anna Karenina; there's his leading role in the forthcoming Star Wars Episode VII; and there was the recent Calvary, in which he had a cameo as a creepy serial killer enduring a prison visit from a priest played by his father, Brendan, an experience he found "really cool". Apparently, they tried discussing the scene, found they didn't agree about its themes at all, and ended up "not talking a great deal between takes on set, and just beating the shit out of each other emotionally for a day".

Gleeson is also extremely good as the lead in the film we're ostensibly here to discuss: Frank. Once you get past the fact that it isn't a biopic about its writer Jon Ronson's time playing keyboards for the late musician and comedian Frank Sidebottom (an easy mistake to make, given Gleeson's character is called Jon and plays keyboards in a band fronted by a man called Frank, played by Michael Fassbender from beneath a papier-mache head almost identical to that sported by Sidebottom), Frank turns out to be a funny and moving meditation on mental illness and the corrupting power of fame, even of the minor variety.

In fairness, Gleeson seems satisfied that he hasn't ruined this one. You would think that acting opposite a man who spends virtually the entire film with his face obscured by a giant papier-mache head might constitute a challenge (co-star Maggie Gyllenhaal was apparently a little discombobulated by the experience) but Gleeson insists he didn't find it a problem. "I read an interview with Maggie where she said she found it difficult to connect to the head, but I think the whole point of my character is that he's supposed to be fascinated with the head. He wants to know what's going on inside it, so that makes it really easy."

Given how well his career's going, Gleeson's apparent insecurity feels a little baffling, although, over lunch in a fancy London hotel, he doesn't exactly come across as a bundle of neuroses and self-doubt. In fact, he's rather jolly company. "Star Wars is different to anything I've done before," he says. "But at the same time, the job remains the same – it has to. So the director, the script and the other actors are the reason to do it, as opposed to the history of the series. But I'd be lying if I didn't admit that the table read was one of my great moments – and not just for work reasons."

He demolishes his steak with the gusto of a man who recently lost 27 pounds in seven weeks for a role in Unbroken, an Angelina Jolie-directed film about second world war hero Louis Zamperini, who survived 47 days on a raft in the Pacific after a plane crash, only to end up in a Japanese PoW camp.

"It turned me into a food pervert," he says. "I was just wandering round supermarkets staring at people buying cashew nuts and thinking, 'You fuckers.' It was fucking awful." Worse, he says, having put himself through all that, he doesn't even know if he's in the finished film. "I finished it and thought, 'If I end up not in that movie, I'm going to go fucking nuts.' But every time you're not the lead, you run the risk of being cut from a movie. So we'll just have to wait and see."

Gleeson is certainly serious about the business of acting: at one point, he embarks upon an impassioned harangue about how "disgusting" it was that less comment was passed on Fassbender's performance in Shame than on the appearance of the actor's penis in the film. But he's also very funny – and so luxuriantly, chirpily foul-mouthed that, on a couple of occasions, I fancy I see the rather demure ladies lunching at a nearby table looking aghast, not least when he announces that the most important lesson he has learned as an actor is to remember that, even if you're the star of a film, you're always part of a team. Or as he puts it: "Don't be a cunt, because you're there every day, and you'll make it miserable for everybody. The guy operating the boom isn't allowed to turn up and just be a cunt, so why would you be allowed to do that?"

Still, his family has something of a history of causing consternation in this restaurant. It was here – "possibly in this very seat" – that his father made the fateful decision to watch his son's writing and directorial debut, a 2009 short called What Will Survive of Us, unaware that this Todd Solondz-inspired work was largely concerned with the topic of anal sex. "He didn't even put headphones on," he recalls. "He just played the file I'd sent him. My younger brother was the lead. So he's sat in here, watching a scene where my brother starts masturbating and screaming, 'Take it up your arse, you fucking bitch.' So yeah, that was good." He sighs. "I just like things that are dark and about sex and also funny."

Gleeson is modest to an almost pathological degree. At one point, he starts telling me that Denis Leary sent him a letter praising another short film he wrote and directed, 2010's Noleen, but then he stops himself short, saying: "Sorry, I've gone off on a thing about how great I am." Perhaps it's all bound up with the fact that Gleeson knows people think he's had something of a meteoric rise, aided by the fame of his father, who gave up teaching to become a full-time actor at 36, and enjoyed his breakthrough as Hamish in Braveheart four years later (12-year-old Domnhall's pride was apparently tempered by mortification that the part required his father to show his buttocks).

At 16, Gleeson was spotted by an agent after picking up an award on his dad's behalf and improvising a speech on the spot. His first major role was in Martin McDonagh's The Lieutenant of Inishmore, which ended up on Broadway and secured him a Tony nomination. But it's hard not to think his insecurity might have more to do with what happened in the aftermath of his initial success. "I came back to Dublin from Broadway thinking, 'Oh man, I'm a full-time actor and people will want me because I got nominated for a Tony.' And there was just a wilderness. Nine or 10 months, not one job, not even a day here or there. I barely had an audition. I know I have it a lot easier than most, so there's no point in pretending it was incredibly tough, but 10 months without work is difficult, and I didn't like it."

He'd watched his father fill in downtime by writing, so that's what he did, coming up with his two shorts and sketches for an Irish TV comedy called Your Bad Self. He still writes, he says, "although the comedy I write is all dick jokes. I'm 30 and my sense of humour hasn't changed since I was 19." He had ambitions to write a full-length screenplay, but they're on hold now that he's been inundated with acting work – the news that he singlehandedly ruins almost everything he's in having seemingly failed to reach the world's directors.

He nods. "Enough people who I love, people like the Coen brothers, Lenny Abrahamson who directed Frank, Richard Curtis, enough of those people…" His voice trails off. "Oh, this will sound really big-headed," he sighs before resuming. "Enough of those people have decided to work with me that I can't be that shit." He frowns. "Or maybe I am. The whole idea with acting is that you take some risks. And if you take some risks, you're really going to mess up sometimes. But it's not OK to mess up a movie, it's not OK to do that just so you can improve as an actor. But film-making takes a little bit of risk in every department. So fuck it. Whatever." He drains the last of his beer. "Fail again, fail better. And all that shit."

Frank is on general release on Friday.