This is beyond strange. Chiwetel Ejiofor is sitting in my kitchen, staring at my wet laundry. I'm trying to act cool, but with the noise of a bawling child upstairs, and my husband clattering pots on the hob, I'm struggling. The opposite is true of Ejiofor, who leaps eloquently from one politically charged subject to the next. He doesn't mention the washing.

OK, he's not strictly speaking actually in my kitchen, but he is on the screen of my laptop, which is sitting on my kitchen table. Minutes earlier, he was in my arms, so to speak, as I carried him through the house to escape the aforementioned cries, although to be fair, he wasn't the one being put off by the squawks.

I'd hoped for more from doing this over Skype: an insight into the famously reserved Los Angeles-based actor's world that a mere phone call wouldn't have provided. A mystery partner, perhaps, calling out to him; or maybe a screen grab of his dog, Clay the Pyrenean Shepherd, bounding over to lick his face. Instead, I get the blank walls of what turns out to be a hotel room in New Orleans, where he's spending a couple of weeks finishing off a film with Steve McQueen about the slave Solomon Northup. So much for snooping.

He's talking race: what it meant to be black and musically talented in the 1930s, something he describes as "not black and white", no irony intended. His latest on-screen alter ego, a jazz musician, tests society's attitude towards blacks at the very highest levels in a new Stephen Poliakoff TV drama, which starts next week.

The series, Dancing on the Edge, exposes the interaction between black musicians and the British aristocracy via a fictional jazz band, led by the pianist Louis Lester, played by the 36-year-old Ejiofor. He loved the role, which was loosely based on the cabaret star "Hutch" (Leslie Hutchinson), finding the "racial concepts" fascinating – "the ideas we perceive now as liberal, and the formation of those ideas at a time when there's a rising idea of fascism and the real polarisation of race and class".

I watch him lean back in his chair, stretching out his arms before adding: "The Second World War simplified things like race, and people came down on very clear lines. I feel like modern-day racial discussions are much more complicated. At any given point, different sides of that argument are winning or pushing their viewpoint forward. 'Winning' in inverted commas. The perception is always that things get more liberal, but that's not always how it works. The investigation of race politics in the Thirties and people's openness had an interesting parallel. Paul Robeson would be playing Othello, as opposed to Laurence Olivier. And even though him kissing Peggy Ashcroft would mean that some people would walk out, some others would think it was brilliant and take it back to the States. But then, 20 years later, that sort of dynamic was impossible for a while."

For his part, Ejiofor, who sprang to fame, aged 24, playing the Nigerian immigrant Okwe in Stephen Frears's Dirty Pretty Things, denies ever finding his skin colour constricting. "I've been fortunate to be able to do a lot of different things. I haven't felt any frustration [about parts he's been able to play]. In certain areas, British films don't have as many black characters [as US films] and in other areas they do."

Dancing on the Edge is the second British television drama that Ejiofor has done in the past few years, following his part as a policeman in Hugo Blick's The Shadow Line, underlining the fact that, although he may be based in sunny LA, the reality is more complicated. "I guess I live ... I don't know ... I live, well, the two places that I spend most time in are London and Los Angeles." I have to bite my lip to stop myself butting in to admit being able to pinpoint his base over here. Not because I'm an Ejiofor stalker, but because he bought the mews house next door to my oldest schoolfriend, in Marylebone.

He spent a large chunk of last year banishing family demons in Nigeria, where he filmed the British-financed Half of a Yellow Sun, based on Chimamanda Ngozi Adichie's brilliant book about the Biafran war. The conflict prompted his parents to flee the country, emigrating to London, where they had Chiwetel, along with his elder brother and two younger sisters. The fighting also uprooted his grandfather, a story Ejiofor captured on tape a few years ago.

"We spent maybe 10 hours talking about the Biafran war and what it had meant to him. He was an accountant in the mining corporation in the north of Nigeria. By the end of the war, he was travelling with his entire family. They were migrating through the east as [the government] was trying to bomb villages. He didn't have anything. Not a penny – a huge turn of fortune from being quite wealthy, to being destitute. He had eight children, and he lost one boy, my uncle Arthur, but everybody else survived. To play somebody almost the same age as my grandfather was when that was happening was really interesting, and emotional."

Nigeria was also the scene of Ejiofor's greatest trauma: a car crash aged 11 while on a family trip back home that cost his father his life and left the young Chiwetel hospitalised for 10 weeks with broken arms, wrists, and head trauma. Not to mention a scar across his forehead. I attempt to tread carefully around the memories, but Ejiofor is blunt. "Maybe the first few times I went back to Nigeria I found it kind of complicated, but you get past that. This is 20-something years on." Cue tough guy voice: "I can handle it."

Indeed, there is something astonishingly self-possessed about the cut-glass accented Ejiofor, who sounds not dissimilar to Poliakoff's well-spoken Louis Lester. Such is the power of a public school education – Dulwich College, where he fell in love with acting. He is the only one of his siblings to tread the boards: his brother works in fashion, while one sister has just finished at London's Imperial College and the other is with CNN in New York.

After New Orleans, it's back to LA, then to the Democratic Republic of Congo, where Ejiofor will research his next big role, as the country's short-lived first independence leader, Patrice Lumumba. Joe Wright will direct him in A Season in the Congo at the Young Vic, in what will be Ejiofor's first London play since he won an Olivier award for his Othello at the Donmar Warehouse five years ago.

I may have conducted the interview in reverse: given him the measure of my chaotic, exhausting life while letting him keep his own under wraps, but I'll settle for the fact that the Hollywood star was in my house. Sort of.

Dancing on the Edge starts on 4 February on BBC2

Curriculum vitae

10 July 1977 Born in Forest Gate, east London. Later moves to Crystal Palace with his parents, who had fled Nigeria's Biafran war, his elder brother, and two younger sisters.

1985 Suffers horrific injuries in a car crash in Nigeria; his father is killed.

1990 Studies at Dulwich College, where he falls in love with acting. Works with the National Youth Theatre, before attending the London Academy of Music and Dance (Lamda).

1997 Makes his film debut, aged 19, in Steven Spielberg's Amistad.

2002 Takes the lead role in Stephen Frears's Dirty Pretty Things, winning the British Independent Film Award for best actor.

2005 Gets a Golden Globe nomination for Kinky Boots.

2007 Wins Olivier Award for his Othello at the Donmar Warehouse.

2008 Is made an OBE. Makes directorial debut with the short film Slapper.

2013 Stars as band leader Louis Lester in Stephen Poliakoff's new drama series, Dancing on the Edge.