There may be a website devoted to matching pictures of otters with shots of the actor (yes, really) but there's something magnetic about being in his presence. Just ask his devoted female fans (the so-called "Cumberbitches"), although he's in denial about this sex-symbol status. "I don't think people turn on to see me, looking the way I look."

Certainly, he slips neatly enough into the ensemble for , which also features Brad Pitt, Michael Fassbender and Chiwetel Ejiofor as Northup. He plays William Ford, "a very paternal slaveowner", who becomes Northup's first master. While he's a kindly soul, Cumberbatch makes no excuses for a man who bankrolls his ailing business with human trafficking. "It's still a terrible thing he's doing. When the chips are down, he sells these people because they are a commodity to him at the end of the day; they can get him out of his debt, and make him solvent."

It recently emerged, in a horrific twist of fate, that Cumberbatch's own Bristol-born ancestors founded their family fortunes on a sugar plantation in Barbados and owned slaves - revelations that came to light via a newly appointed city commissioner in New York, Stacey Cumberbatch. Not that the actor has ever tried to hide his family's dark secret. In the past, he claimed playing abolitionist prime minister William Pitt the Younger in the 2006 film was a "sort of apology" for such events.

With brutal realism, McQueen's drama doesn't flinch in its depiction of the slave trade. "There was a massive black market," the actor says. "Their value increased beyond the actual value of the land they were cultivating, and the produce they made. So they were traded for thousands of dollars, and were farmed themselves and brought together for their fertility. Families were kept together to try to breed children, [who could then] be nurtured into slavery, in adolescence and adult life."

Family is also at the dark heart of , with Cumberbatch once again joining an A-list ensemble in a US-shot production. An adaptation of Tracy Letts' Broadway hit about the Westons, a dysfunctional Oklahoma clan, it's the sort of scenery-chewing drama tailor-made for the likes of co-stars Julia Roberts and Meryl Streep. But Cumberbatch is just as vivid as the tentative cousin "Little" Charles, frequently derided by his overbearing mother.

A fan of the Pulitzer Prize-winning play, he was desperate to enlist. "When I heard they were doing it, I thought: 'I've got to audition! I'd kill to play that part!' Are you kidding me? To sit around that table and watch Meryl?" He even self-taped an audition on his iPhone and sent it to John Wells - another director only dimly aware of the Cumberbatch canon - to get the chance to hang out with the "astonishing" Streep. It's charming, seeing this erudite actor suddenly reduced to a quivering fanboy at the mention of her name.

Cumberbatch was geared towards acting from a young age; his parents were both actors and enjoyed long careers in film and television. When he won a scholarship to the elite Harrow School, he joined The Rattigan Society for the dramatic arts. After a gap-year teaching English at a Tibetan monastery, Cumberbatch went to the University of Manchester to study drama, and followed it with a spell at London Academy of Music and Dramatic Art (Lamda).

After leaving Lamda, Cumberbatch began a three-pronged attack on stage and screen, both small and big. He played theoretical physicist Stephen Hawking in TV movie . On stage, his role as Tesman in a 2005 production of led to an Olivier Award nomination. And in cinemas, he proved he was capable of comedy, playing the stuck-up team leader in .

Things didn't really take off, however, until 2010, after the first season of , the BBC's hugely popular revival of Arthur Conan Doyle's genius detective. "I had a perfect storm in that year," reflects the actor. "It did explode." And then some, with roles arriving in Spielberg's , the sublime film adaptation of John le Carré's and Boyle's production of at London's National Theatre.

In all this, Cumberbatch has carefully managed his career, avoiding repetition. "I haven't done back-to-back period dramas, which I could have done, having done my first. I could have done back-to-back smart scientist roles, having done my first. I could have done back-to-back sci-fi, having done my first. You get asked to do what you're most recently famed for. So I'm just careful of not repeating myself. But over the course of my career, I have casually gone back to those things, but it is circumstance really."

Is there anything that would stop him returning for a fourth series of ? "Losing my memory; it happens when you get older!" he quips. "No, not that I can think of - I'd love to keep doing it." Before that, there's a reunion with his co-star Keira Knightley on , playing second world war Enigma code cracker Alan Turing. Confidence is such that he isn't even concerned about the work evaporating anytime soon. "I'm not nervous of it drying up," he says. "I've always had an eye on longevity; I've got loads more goals to achieve. It's not like I've completely conquered the whole thing; that's a lifetime's objective, not an overnight thing." If Cumberbatch has his way, that "moment" he's having will last a very long time.

12 Years a Slave August: Osage County