The scouse star of Boardwalk Empire and This Is England has made a career out of portraying the kind of men you'd cross the street to avoid. He's a pussycat, really. But rudeness risks a slap

That Stephen Graham has kicked, punched, stamped and spat his way into the public consciousness is made all the more strange when you discover that in reality, he's possibly the nicest man in the business. As he explains his decision to take his wife, children, parents, brothers and friends for a holiday to Hawaii while he was there shooting Pirates Of The Caribbean: On Stranger Tides ("It's something you have to share"), it's hard to associate him with his current incarnation in HBO's epic crime drama, Boardwalk Empire, in which Graham plays a stocky, violent little driver for the Chicago mob named Alphonse "Al" Capone. And it's even harder to see how he managed to channel Combo, the racist thug from Shane Meadows's This Is England and This Is England '86.

In person he seems to be constantly on the verge of inviting you round for dinner. So how does the 37-year-old married father-of-two from Kirkby, near Liverpool, manage to portray such bad men?

"I just have a knack of being able to tap into those kind of characters," says Graham. "I find them interesting people to play; I always have to find a redeeming feature. There are certain events in my life I can think about when I'm beating someone up, but that's my own little thing. It's mostly about believing in the character."

This Is England. Photograph: Bfi

After paying his dues in gentler pre-watershed dramas such as The Bill and Heartbeat, Graham was cast as Tommy, the gormless right-hand man to Jason Statham's boxing promoter in Guy Ritchie's Snatch. This in turn led to a role in Band Of Brothers, the unofficial incubator for British male character actors having featured – deep breath – Damian Lewis, James McAvoy, Simon Pegg, Dexter Fletcher, Marc Warren, Jamie Bamber and Tom Hardy as varying grades of cannon fodder.

Next came a brutal turn as a member of The Dead Rabbits alongside Leonardo DiCaprio in Gangs Of New York, the role that first bought Graham to the attention of Martin Scorsese, who would cast and direct him again in the pilot of Boardwalk Empire.

But it was bovver-boy Combo in This Is England that really cemented Graham's place in the annals of celluloid psychopaths. For the majority of the film he exudes the kind of calm menace you might see in a pitbull terrier dozing on the roof of a pub. It's only in the final reel that he suddenly, and without much warning, perpetrates the kind of brutal act that leaves you struggling to remember that the film is supposed to be entertainment. It's this ability to combine a smile with the possibility of extreme violence that means he was first in line for the plum role of Capone in HBO's hooch and harlots saga.

"The whole thing was surreal," recounts Graham. "My manager said he'd had Scorsese's people on the phone, and Marty wanted a quick chat. So I got a phone call off him and he's asking, 'How's life? How are the kids?' Then he says, 'I want you to play Al Capone.' Well, you don't say no to that."

Public Enemies. Photograph: Allstar

Graham then spent six months working alongside Steve Buscemi's sublime Enoch "Nucky" Thompson, a corrupt politician who controls the bootlegging in prohibition-era Atlantic City, and Michael Pitt's up-and-coming ne'er do well, Jimmy Darmody.

The show's creator, Terence Winter, a former producer and writer on The Sopranos, wanted Graham to create his own interpretation of the famous gangster, giving him free rein to flesh out the young Capone as he finds his feet and fists in the criminal underworld.

"Terry wanted me to come up with my own version of Al," he says. "At the beginning he's just a young thug. By the end of the series, you start to see the signs of the man we're all familiar with."

To prepare for the role, Graham researched the early years of the Brooklyn-born Capone and found that, even from an early age, he showed menacing potential. "When he was growing up, Al and his mates used to watch the soldiers doing their passing out parade," says Graham. "One day, they were taking the piss out of this sailor because he kept messing up. Eventually the guy came over, and despite the fact he was only 11, Al wanted to beat this guy up. In the end the commanding officer broke it up and asked if he thought he could do better. So Al just turned on his heel and did the whole routine perfectly. The commanding officer apparently sent a letter to the head of the naval base, saying, 'I've just seen a young kid today, Alphonse Capone. I think he could either become the best soldier we've ever seen, or I dread to think what might happen.'"

Graham recounts stories about using a toy golf club as a gun to audition for Michael Mann's Public Enemies (he played Baby Face Nelson), and the time he taught Daniel Day-Lewis to play the card game Shithead between takes on Gangs Of New York. It becomes clear that the reason he's able to marry the loving family man with the fiery little bastard you'll have recently seen wrapping a bottle of bourbon round the head of a journalist in a speakeasy, is because he's very good at his job, and more importantly, he's having an absolute blast.

Boardwalk Empire.

"It's a dream come true to be on this big set, being directed by Martin Scorsese again," he says. "It's certainly a long way from getting the bus with my mum to the Everyman Theatre in Liverpool. A friend said, 'You should give yourself a pat on the back, it's what you've always wanted.' But you can't think like that too long or your head goes up your arse and you turn into a knobhead."

Despite the humility, it seems he isn't completely innocent. A little bit of Capone has found a chink in Graham's cheery armour.

"I like him. I really like him," he says with a mischievous grin. "There's this scene in the show where we get these beautiful suits fitted, and an extra had come in for the day to play the tailor. We were sitting there before the take, and this young girl asked if we wanted anything, and he said, 'Tea. Milk no sugar.' So she bought his tea over, he took a sip, and spat it out saying, 'I said no sugar!' He did this right in front of everyone, and I just thought, 'You idiot.'" He stifles a guilty laugh before continuing: "So later, we're doing the scene, and we've got these suits on, and all of a sudden I really, really felt like Al Capone. So I looked at the extra and smiled, and he looked at me, and I slapped him round the face and then carried on the scene. The director yelled cut, and the whole crew burst out laughing. I just calmly said to him, 'It's nice to be nice.' You'll see it in the scene. Just watch his face."