Upwardly mobile: David Oyelowo on going from Tooting Bec to Tom Cruise's jet

Growing up on an estate in Tooting Bec, south London, actor David Oyelowo's father used to claim that he was Nigerian royalty. "The only barometer I had for that was our royal family here, so I was 'What are you talking about?'," recalls Oyelowo, who was six when he discovered that his papa was not actually a Walter Mitty figure, after the family relocated to Lagos. "We were met at the airport by this line of cars and driven to Oyelowo Street," he says, adding that: "It sounds way more impressive than it actually is. There are so many royal families in Africa – it's like having royal families of boroughs of London – the king of Hackney, say, or the king of Islington."

The king of Islington. That sounds fun, I suggest, and Oyelowo – pronounced as if there were an 'o' on both sides of 'yellow' – gives a smile as wan as the winter sunlight outside the Westminster hotel where we meet. Wrapped up in scarf and elegantly chunky knitwear against the British weather, he's on a two-day visit to the UK from his home in Los Angeles, and isn't bothering to try and sleep off his jet-lag. In the circumstances he's remarkably friendly and engaged, and indeed just a bit regal, which is perhaps why, at the age of 24, he became the first black actor to play an English king in a major production of Shakespeare – in the RSC's Henry VI, where he was referred to as "the black Olivier". "I was, 'Mmm… I don't know how I feel about that'," he says. "I was very keen to find something to oxidise that quite quickly, and Spooks was perfect for that."

Ah, yes, Danny Hunter in Spooks, who, like many another character in BBC1's hi-octane spy saga, met a sticky end (his at the hands of Iraqi terrorists). It was at this juncture that Oyelowo decided another radical change was necessary, moving his family (wife Jessica and four children) to the San Fernando Valley in California, erasing any last traces of that 'classical actor' tag with such diverse Hollywood movies as Rise of the Planet of the Apes, The Help, 96 Minutes and The Paperboy. And now he is a prince among Tinseltown royalty – filming car chases with Tom Cruise in Jack Reacher and lecturing Daniel Day-Lewis in Lincoln – once on the same day, necessitating a trip in Cruise's private jet. In the middle of a three-week night-shoot in Pittsburgh for Jack Reacher, which involved a car chase where Cruise, as usual, did his own driving, Oyelowo also had to put in two days filming on Lincoln in Virginia.

"But nobody had told Tom," he says. "I was in Richmond, Virginia, with Daniel Day-Lewisf and Spielberg having the time of my life and I start getting these calls saying, 'Tom's really excited about this car chase tonight' and I was, 'What are you talking about? I'm here' – and I'm not going to be the one to tell Spielberg I'm leaving. Goodness knows what happened behind the scenes but I was on a jet that took me to Pittsburgh and I walked straight into that car chase."

Heady times. The role in Lincoln is a minor one, as a Unionist cavalryman who challenges Lincoln about his Gettysburg Address, but it gave Oyelowo the chance to observe his acting hero, Day-Lewis, in close-up. "He is in character all the time," says Oyelowo. "You have to call him 'Mr President' or 'Mr Lincoln' if you're going to address him. He was the acting equivalent of a time machine for me – just being around him you sank right into 1865. I was talking to Sally Field about this the other day…"

Now if that reads like name-dropping, it's not how it sounds when he says it. In fact, there's only one individual who seriously awes Oyelowo and that's the Big Man – God – but more about that long-term relationship later, for after his run of high-profile supporting roles in America, Oyelowo has returned to these shores to take centre stage in a Channel 4 drama, Complicit. He's in every single scene, playing an MI5 case officer who begins to suspect that one of his surveillance targets – a Muslim taxi driver – is plotting a terrorist attack on London. An absorbing character-study which covers much of the same philosophical terrain as Kathryn Bigelow's hunt-for-bin-Laden drama Zero Dark Thirty, Complicit is also like a cerebral and understated double-episode of Spooks.

"When I spoke to real MI5 officers, I heard this is way more indicative of what they do day in, day out… Spooks was more like an hour of Bond for the telly," he says. "Complicit also looks at the class system within our country and that's what I loved about it… these layers – on the surface of it there's a cat and mouse, but there's this whole internal issue about what university you went to and so on."

Having lived in LA, Oyelowo understands that America has its own class system – one based on money rather than old-school ties – but on the question of race, he believes the formative years that he spent in Nigeria, between the ages of six and 14, gave him a healthy perspective. "It was amazing to live in a country where I wasn't a minority," he says. "It gave me a great sense of self that has served me well… coming back to the UK and more especially America, where the lack of identity that a lot of African-Americans feel plays into an inferiority complex that really does affect their world view, and not in the best way."

Having attended a strict, "military-style" boarding school in Lagos, where regular beatings instilled respect for the teachers ("none of this softy-softy stuff we have here"), the corruption in Nigeria finally became too much for his parents, who returned to London – this time to Islington, where he suffered severe culture shock at the local comprehensive.

"The kids were swearing at the teachers," he says. "It was free education and yet so many of them didn't want to be there, they were bunking off, and I just felt to shocked because I had watched my parents work themselves to the bone to send my brothers and me to the best schools possible. I was, 'Can't you see how amazing this is?'."

They couldn't, and for his pains Oyelowo found himself on the sharp end of bullying from black classmates who dubbed him "a coconut" – black on the outside and white on the inside. It was an experience of "weird internal racism" that was to feed into his searing performance in the 2006 BBC drama Shoot the Messenger, in which he played a teacher falsely accused of assault by a black pupil. "The film was very uncomfortable for a lot of black people," he says. "This phrase kept coming up that this was somehow 'airing our dirty laundry'. I'm a big one for airing our dirty laundry… I think that's the only way to get it clean."

The teenage Oyelowo found escape in youth theatre, lured there by what he thought was the promise of a hot date. "She was myf pastor's daughter," he says. "After all this time of fancying this girl… she came up to me after church and said, 'Do you want to go to the theatre?'. It was so embarrassing… I turned up at Finsbury Park tube station with a rose and as I walked towards her I could just tell I'd got this wrong."

She took him to the National Youth Theatre, which eventually led to his first performance, as the lead in a two-night production at the Cottesloe. His father, Stephen ("one of those perpetual African students") had wanted him to become a lawyer, and Oyelowo had a place lined up to study law at Oxford Brookes University when a chance encounter at Holloway tube station with his A-level theatre-studies teacher changed his destiny. "She said, 'David, I wouldn't say this to everyone, but I really think you could have a career as an actor'. She then helped me with all my auditioning… I didn't know what drama school was – and I ended up getting a scholarship to Lamda. That was the only thing that swung it for my dad, the scholarship… 'My son the scholar'," he says, putting on a Nigerian accent.

"The moment where I knew it [acting] was OK with him was when he came to see me playing Henry VI at the RSC. He came up to me at the stage door and said, 'When I first moved to this country, there was just no way a black man was ever going to play the king of England at a place like the Royal Shakespeare Company, and it's my son?' It was deeply moving for me."

By now Oyelowo was married, having met Jessica Watson, as she was then, at a summer youth-theatre production of Brecht's Threepenny Opera when he was 17 and she was 19. "She was shambolic," he recalls. "A head of huge hair – you could hardly see her face… terrible posture… and then she sang and it was just like a thunderclap. We became friends for quite a while and it became clear that we were just kidding ourselves and we got married."

Both are committed Christians, Oyelowo having been raised a Baptist. "But at the age of 16 I realised that I was pretty much piggy-backing on my parents' faith," he says. "So I did this really naive, odd thing which was to say, 'OK God, if you exist, I'm going to go to a different church because I find mine very boring, and if You don't turn up for me in three months I'm done'. And for me He turned up in a very palpable, undeniable way."

How so? "I literally heard God speak to me about how much He loved me. That voice never abated. Like any relationship, it becomes deeper. It's a hard thing to explain – it's like explaining love to someone who has never fallen in love."

I had read somewhere that he prays for advice on which movies to take. "All the time," he says cheerfully. "Sometimes I don't like the answer, but sometimes it's when He crosses my will that it is the most useful. In what I do for a living there are pitfalls like money, fame, attractive people…"

The latest roles that Oyelowo has cleared with the Almighty are as singer Nina Simone's manager and lover, Clifton Henderson, in the biopic Nina, and a part in The Butler, which is based on the true story of Eugene Allen (played by Forest Whitaker), the White House domestic who served eight different Presidents. "Oprah Winfrey plays his wife and I play his son and the film is largely about the juxtaposition of him in the White House and me becoming a civil-rights activist."

Next is a biopic of boxer Sugar Ray Leonard, made by the producers of Moneyball and the third in a succession of specifically black roles. It's not entirely what Oyelowo had in mind when he followed fellow black British thespians Idris Elba, David Harewood and Lennie James to America in order to break through a perceived glass ceiling. "It's exacerbated for a black actor in that the stories that we tend to tell in this country, a lot of them are period dramas; we seem to be in denial about how long black people have actually been here."

He's keen to see more black characters who aren't just rooted in race. "I'd read somewhere that Denzel Washington said to his agent early in his career, 'I want you to put me up for everything that Harrison Ford is turning down', and that really stuck with me. Ultimately that's all every actor wants to do, to just be allowed to portray humanity as opposed to ethnicity or skin colour."

'Complicit' is on Channel 4 on 17 February