Stephen Graham on This Is England, Boardwalk Empire and Hyena

Odd that, since the Scouser has made his name playing some of the toughest nuts around, including This is England's racist skinhead Combo, and a young Al Capone in Boardwalk Empire. Graham's new film, Hyena, finds him playing a cop so bent he makes a boomerang look like a spirit level.

"Don't make me out to be a soppy little t***," counters the man himself. "Yeah, I'm slightly sensitive I would say. I'm in touch with my feminine side."

These sentiments are delivered with a laugh over morning tea in a smart Edinburgh hotel. Classical music is playing, the capital's ladies are rattling the bone china fit to beat any passing brass band, and I am teasing Graham about how often he seems to cry. It is a brutal business but someone has to do it. Having lived for a time in Liverpool I have, like all honorary Scousers, a licence to wind up, or, as they say in Bleasdale country, to "skit". Glaswegians, world-class slaggers, will understand.

Graham, 41, is in the capital to see Hyena, a crime drama written and directed by Gerard Johnson, which opened last summer's Edinburgh International Film Festival. The picture goes on general release next Friday. Featuring Albanian gangsters, people trafficking, drugs and corruption, Hyena is The Long Good Friday for our hell-in-a-handcart times. Dixon of Dock Green, or even The Sweeney, it ain't.

"It's not car chases and 'Awright son, you're nicked'," agrees Graham. "There's none of that in it. It's a very honest film." Are people ready to look on the police this way? "I think we should," he says. "Look at what happened with Hillsborough. From the top right the way down things are going on that... there's a lot of corruption there and a lot of things happening that we are not aware of until these investigations happen later on." He reigns himself in and returns to the subject of the film. It is early on in our interview, the tea is still hot in the cups, and he is wary of straying too far off course.

Later this year, Graham will be seen again on Channel 4 in This is England '90, the final part of Shane Meadows' multi-Baftas winning drama that started with the 2006 film. Before playing Combo, Graham had enjoyed a steady but unspectacular acting career. He first acted with the Everyman Theatre's youth section, and was swithering between becoming a firefighter or an actor when a part came up in Coronation Street (he played Lee Sankey, resident of HMP Strangeways and friend to Steve McDonald).

His British movie breakthrough came with Snatch, the 2000 crime caper directed by Guy Ritchie and starring such geezers as Jason Statham, Vinnie Jones, and, er, Brad Pitt. From there, he became one of the posse of British actors, alongside Jim Broadbent, Daniel Day-Lewis, Scotland's Gary Lewis and Eddie Marsan, who were cast by Martin Scorsese for 2002's Gangs of New York. He made an impression on the Goodfellas director.

"When we did Gangs of New York he said to me, 'I'll find you something, we'll do something again.' I was like, 'Don't say that unless you mean it.' True to his word, it was a long time after, five, six years later, I got a phone call in the house. My agent. Will you be in for the next 20 minutes, Martin Scorsese's office are going to phone. He phoned and said do you fancy playing Al Capone?"

And so a young young Alphonse Gabriel Capone was born to do business with Steve Buscemi's Nucky Thomson. The Golden Globe and Emmy winning series, set during the Prohibition years in America, is champagne for the eyes. "It's very lavish, like the era itself," says Graham.

Portrayals of Capone are many and variable, from Robert De Niro's take on the character in The Untouchables to Rod Steiger's in Capone. But nowhere has he been seen, as in Boardwalk Empire, in criminal embryo.

"Because we had the chance to create him from a young age we could put a lot of things into that character that people hadn't seen. I'd read so many books about him, it was like being back at school. I had a big file at home with what he was like at certain points, the timeline of his life." Capone had a wicked sense of humour, says Graham. Would he have liked to have met him? "I don't know. I don't know if he'd have liked me," he laughs. "I wouldn't sit down and have Sunday dinner with him, but it would have been interesting to meet him. He is a charming psychopath."

While making Boardwalk Empire, the fifth and final season of which is now out on DVD, Graham would decamp from Leicestershire (where he lives with wife Hannah Walters, also an actor, and their two children, Grace and Alfie, ages 10 and eight), to Brooklyn, where the series was shot. An actor's life for him has always meant travelling, whether it was taking the bus to the Everyman in Liverpool from his home in Kirkby when he was a youngster, or Glasgow, where he made American Cousins in 2003. He knows Glasgow fairly well from that visit, and others he has made subsequently, including one in 2013 to take part in a match in aid of the Stiliyan Petrov Foundation, the charity set up by the former Celtic player to improve cancer treatment. Graham's pal, the Scottish actor Martin Compston, asked him to play. Graham is big on loyalty. Take Thomas Turgoose. Graham met the then 14-year-old on This is England. Turgoose played Shaun, the fatherless lad who initially idolises Combo. Today, Turgoose jokingly calls Graham and his wife nana and grandad, and visits regularly, which is pretty decent of him considering what happened in one of the more notorious scenes in This is England, the one where Combo beats someone to a pulp.

"That was heavy to film," says Graham, then breaks into a smile. "The worst thing was the fact that we didn't tell little Tommo." Turgoose knew that someone was going to be hit a few times, but not to what extent, so his horror is the real deal. "It was Shane's idea and I'll never forgive him, I've told him I'll never forgive him because Tommo hated me for two days."

All of this is said while laughing. It has clearly become a running joke between Graham, Meadows and Turgoose. But then Graham grows quiet for a moment as he recalls Tommo's face. "I feel like crying already. The emotion of that young lad seeing this horrific thing, but it's his reality. I said it was wrong." Now he is laughing again. "I said I'm having nothing to do with this but we did it. We did it. He hated me all day." By this point we are both cackling. Scousers and Glaswegians, eh?

The other scene for which Graham will be remembered is the one in the car where Combo, just out of prison, confesses his feelings for Lol (Vicky McClure). In the space of minutes, Graham, his face registering a rush of emotions in infinite shades, turns in a piece of acting that, had this been a Hollywood movie, might have made him a shoo-in for an Oscar. "I don't watch stuff I'm in that often, but I've seen that film a couple of times and that bit in particular always makes me feel a bit sick inside."

He remembers finishing the scene and getting out the car to a set that had been struck dumb. "I went, 'It's all right, I'm okay, I'm fine, don't worry about it'. I thought I was OK then I had a little weep and stuff. Sometimes you can't really explain it. Something happened and for that particular moment in time I was that man. Not meaning to sound pretentious, but something happened. But it was the environment that was created for something to happen."

Aside from the intensity of the role, there was another reason why Graham spent so much time damp eyed during the This is England shoot, including after the scene where he racially abuses an Asian shopkeeper. Graham's grandfather, you see, is Jamaican, his grandmother Swedish. The family is mixed race. To call his portrayal of a racist thug a stretch, a leap above and beyond acting duty, would be a gross underestimation. He was in two minds about telling Meadows about his grandfather, fearing it might complicate things and cost him the part. Meadows reckoned it made him perfect for the role.

I ask him if the family experienced racism when he was growing up but Graham downplays the notion. "Slightly. Not over dramatically. There were a good few incidents that happened. To me as well. Little things happened to me. To my dad there were slight bits of racism growing up. It's changed a lot now. It's still there, it still exists. Look at that ridiculous ... who is that party that's kinda like the BNP but dressed up nicely?"

Of these incidents he would rather not go into any detail. There was, he says "nothing that scarred or affected me for life". He is similarly keen not to dwell on an incident that happened 15 years ago when he went home and was the victim of an attack outside a club. "One silly young man with a chip on his shoulder. Which can happen anywhere in the world."

Later, he tells me about the shop scene in This is England and how he embraced his fellow actor afterwards, crying and saying sorry. It is time to address the blubbing issue. He's quite an emotional person, is he not?

"I suppose I am a little softie, aren't I? Why do I play all these psychopaths that kill people and everything? I don't know. My mum goes, 'I can't wait for you to play a decent man'."

Has he ever watched Bambi without crying?

"Yeah, but I can't watch the Color Purple all the way through without crying."

Through Gangs of New York and Boardwalk, Graham has been adopted by the business in America like few others. He counts Leonardo DiCaprio a friend, for example. They met on Gangs and have stayed in touch since. One recent outing involved Graham, a rap fan, asking DiCaprio to drive him around the gang-dominated area of Compton in Los Angeles. The cops pulled them over, and advised DiCaprio that maybe this wasn't such a good idea. They asked for his autograph too, of course.

Graham can trace his loyalty instinct back to his Merseyside childhood. His mum, a social worker, and dad, a paediatric nurse, brought Graham and his two brothers up within a network of aunties, uncles and cousins. Never a door was closed to them. "I'm very proud of where I come from. But what's made me the kind of person I am is my family." This was Graham's gang, the kind of support system that enabled him to disregard the advice of his careers teacher and take a punt on acting. He thinks back to 2011, when he was cast in Pirates of the Caribbean. The producers rented a house in Hawaii for him, and he flew his family, including mum, dad and brothers, out.

One day he was going to the set and had what he describes as epiphany. "I was in this wig, pirate stuff, my hair is blowing in the wind and I'm on a speedboat, bouncing up and down. I just sat there for a second and thought wow, remember that kid who thought I wonder what it would be like being an actor? That was a moment when I thought you haven't done too bad lad, have you really?"

Boardwalk put him not quite on Easy Street, but a long away from Desperation Avenue. But like any actor he will always wonder what lies ahead. "There are always worries about what's next. Will I get found out one day, how have I got away with this for this long?"

He still thinks that? "Of course you do. The first day on everything I do, the very first day, I always come home and think I can't act."

Interview almost over, out comes the phone to show a picture of his son. As for what this parenting lark is all about, Alfie, your dad believes in keeping it simple and effective.

"Just give them lots of love and lots of enthusiasm. Why not aim as high as you can? I did and it seems to have been all right for me."

Hyena (18) opens in cinemas on March 6.