The septuagenarian walking slowly through the Novello theatre in London looks like an archetypal American tourist. Tall and wide, he wears a puffy gilet that makes him seem even bulkier, while a faded baseball cap shades his face. Yet this ordinary-looking man is one of America's pre-eminent actors: James Earl Jones. Over the last 50 years, he has won two Tony awards (playing a boxer in The Great White Hope, and for his role in August Wilson's Fences), an Oscar nomination (for the film of The Great White Hope), as well as multiple Emmy nominations and awards for his TV work.

You wouldn't know any of this to look at him, because what Jones is most famous for is his voice. Deep, rumbling, august: it's the sound Moses might have heard when addressed by God. No wonder George Lucas chose Jones for the fearful voice of Darth Vader in Star Wars.

Jones, who is about to star in Tennessee Williams's Cat On a Hot Tin Roof, likes to be anonymous. He thinks of himself as a "journeyman actor", quietly muddling along. "Denzel Washington, Sidney Poitier, Robert Redford, Tom Cruise: those guys have well-planned careers. I'm just on a journey. Wherever I run across a job, I say, 'OK, I'll do that.'" He's not too grand to do adverts, either. "I love doing commercials! Usually, they have enough money that they can take time and photograph it well. I'd like to film a British commercial; they're better than American ones."

His stay in London is long enough – Cat is booked until April 2010 – that he may just get the chance. The production transfers from Broadway, where its four-month run was hugely successful with audiences, despite reviews that found it sentimental (the New York Times) and lacking in soul (the New Yorker). There have been some key cast changes: Brick Pollitt, the alcoholic around whom the play revolves, is played here by Adrian Lester, who hasn't been seen on a London stage since his electrifying performance as Henry V at the National in 2003. Jones plays Brick's father, Big Daddy, and while he's aware that the casting switch is having a subtle effect on his performance, he says one thing remains constant: "Big Daddy loves this other human being. It's not like the way I love my own son . . . " He glances warmly at Flynn, his 26-year-old son and assistant. "But I can experience the stage relationship because I have a real son, and that relationship has gone through all kinds of changes and conflicts, but is always enriching."

For Jones, it's the family relationships in Williams's play that count: the fact that this production features a black family, rather than the usual white family, is immaterial. A change of date has been necessary, because when Cat was written, in the 1950s, black people living in the south didn't have the freedom to be as prosperous as the Pollitt family. But apart from that, says Jones, "We're not doing anything to this play that a white family, or a Chinese family, wouldn't do." To argue that Big Daddy is written as a "redneck", a rough and generally rural white southerner, is spurious, as far as Jones is concerned. "I am a redneck, too. I am a Mississippi farm person. I can be foul-mouthed, I can be inarticulate. It's just that my neck doesn't get red. I've always felt that I understood Big Daddy more than the average northern-American Caucasian actor." The New Yorker agreed, relishing the way Jones relaxed into Williams's poetic language.

Born in 1931, Jones spent his first five years in rural Mississippi, living with his maternal grandparents while his mother looked for work (his father, Robert Earl Jones, left before he was born). It was a big household, with 13 people, and for a while it was thought that Jones might live with his paternal grandmother in Memphis "to ease the burden". But when he was driven to her house, he clung to the car. "It was the only way I could express that I wanted to be with them. They accepted that." Soon after, Jones moved with the family to Michigan; the turmoil was so traumatic he developed a stutter that lasted into his teens.

It was his struggle to overcome the stutter that led Jones into acting in the early 1950s. It made him appreciate the value of the spoken word. There were other factors, too: he had just left the army and wasn't sure what to do, while his father, whom he had recently met for the first time, was already acting, having given up boxing. Jones moved to New York to study drama, and lived with his father for a time – not, he says, to reclaim him as a parent, but because he was trying to save on rent. "It was too late to get to know him as a father: if you don't learn that from the beginning, there's no way to catch up. It took us a time to accept that if we could be friends, that would be best. He told me, 'I can't make a living doing this, so if you want to enter this world, do it because you love it.' That was good advice."

After a few years, Jones considered giving up acting, but two things encouraged him. The first was his father's response to one of his performances, in Of Mice and Men. "He said, 'You can act.' He didn't say, 'You were great', or 'You've got potential.' Just, 'You can act.' Father to son, that's all I needed to hear." The second was winning the lead role in The Great White Hope in 1968. "I thought, 'I can raise a family on this kind of work.' That was the key thing: anyone can bum through as a bachelor, but to raise a family you've got to make sure you can draw a paycheck."

Jones's apprenticeship coincided with a period of experimental and political ferment in New York theatre. For Jones, it was the "age of everyman", when people such as Marlon Brando became stars. "You didn't have to be upper class to be a giant of the theatre." In the 1960s, casting black actors in Shakespeare was radical, yet some of Jones's earliest performances were in the New York Shakespeare festival. The play that got Jones noticed, in 1961, was Jean Genet's piece The Blacks, in which black actors perform in white-face to subvert colonial racism. That led to a number of roles exploring African-American life, from The Great White Hope, inspired by black boxer Jack Johnson, to a play about Paul Robeson in 1977; and, more recently, his portrayal in 2006 of Thurgood Marshall, the first black justice of the US Supreme Court.

Although he has been integral to the development of black theatre in America, Jones is resistant to such categorisation. "There haven't been enough profound things written about what being black means, and what a black character is. Nobody knows." He has great respect for August Wilson and his examinations of African-American 20th-century experience, but feels troubled that "to cook up his creativity, August piled blackness around himself. He's half-white, and I never understood why he had to dismiss that aspect of himself."

Jones, who has Irish, Native American and African in his makeup, turns questions of ethnicity on their head. "When you wake up in the morning, before you look in the mirror, do you see an ethnicity? I don't – and if I did, I'd be in trouble, because that has blinded me to who I might really be. Even waking up seeing myself as a male blinds me to who I might really be."

New knees and a farm upstate

He likes theatre to be confrontational: "I don't think we exist as actors just to make people feel good. Tennessee Williams believed in that: he wanted to get under the skin." Off stage, however, he shuns political engagement, and is wary of expressing political views. Mentioning his admiration for the way Barack Obama is "giving Afghanistan the consideration it needs", he immediately apologises for bringing the subject up. Partly, he feels hampered by his speech impairment: "I'm still a stutterer. It affects how articulate I can be in every form of communicating."

He occasionally searches for words, and questions whether he has chosen the right one, but otherwise you wouldn't notice. Yet there is another factor: Jones's father was blacklisted during the McCarthy era by the House Un-American Activities Committee, and felt "he had wasted a lot of energy in the left, because it was badly managed". Jones didn't want to make the same mistake, avoiding Malcolm X's civil rights campaign as he suspected it wasn't well planned.

Despite a long career spent moving between Broadway and Los Angeles, Jones remains humble. Home is a farm in upstate New York, where he lives with his second wife Cecilia Hart, and Flynn, their only child. He has built the place up, adding barns and cabins whenever he had the cash; money might have been less of an issue had his voice work on Darth Vader earned a percentage of the profits, rather than one-off payments.

It's no longer money but his enjoyment of "having a steady job" that keeps him working. At 78, there are certain health issues: "I have new knees. My hearing is going, but I can still see fairly well." For now, he is happy to play any old person role that comes along – even if that mostly means playing people who, like Big Daddy, are facing death. He does have one complaint, though: "Why are people embarrassed about elderly sex? I hate it when I'm given a script in which the guy's wife is dead. That's just an easy way to dispense with having sex. Audiences don't want to see Big Daddy and Big Mama in bed – but I like to talk about it."