However, he's now revealed to The Sun that he struggled to get an audition - let alone land a role - following his performance in 2006 movie This is England.
Graham played racist ex-prisoner Combo in the film, a skinhead with erratic, violent tendencies. Near the ending, Graham beats-up Milky, the only black skinhead in leader Woody's gang.
"It was life-changing. I lost myself quite a bit within that character," he said.
The role was so powerful that it affected him after each day of filming had ended. "I had moments of getting back to my apartment (...) and crying my eyes out, and I drank."
The themes of racism and violence have also affected Graham's personal life. "I'm mixed race. As a kid I was called horrible words that I don't even want to say, and little monkey boy," he said.
Him, his wife and his dad were also attacked by a gang in 2002, leaving them with severe injuries. "It was a completely unprovoked attack - there were about nine of them," he recounted.
Following the movie, he nearly gave up with acting altogether. "After This Is England I could not get a job. For about eight months I couldn't get an audition."
"I almost packed it all in. I was going to be a youth worker."
Fortunately for us Line of Duty fans, he didn't. Graham plays DS John Corbett in the newest series.
Line of Duty continues tonight (April 21) at 9pm on BBC One.
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