WHAT makes man-of-the-moment Benedict Cumberbatch so good at playing odd characters?

"I look slightly... No, I'm not going to call Alan slightly odd!" the 38-year-old Londoner says, referring to the character he plays in his new film. "I don't know. I think they are stories we are all drawn to, really."

His distinctive looks and polished performances, including WikiLeaks founder Julian Assange (in 2013's The Fifth Estate) and Frankenstein (in Danny Boyle's 2011 adaptation at the National Theatre) have earned him legions of fans.

Many were at the premiere of his latest movie - with one waving a sign proclaiming 'Benedict for an Oscar' - in which the actor, who recently announced his engagement to director and actress Sophie Hunter, plays the Second World War codebreaker and "odd fish" Alan Turing.

You'd be forgiven for drawing comparisons between this role and Cumberbatch's famed alter ego, the maverick detective Sherlock.

Both are eccentric, brilliant-minded outsiders, but as the actor - sounding not unlike one of his genius characters - insists, "the kind of Venn diagram crossover or intersection is quite narrow".

Sipping on coffee, Cumberbatch, who confesses his "head's in [the Battle of] Bosworth" after playing Richard III in an upcoming TV drama, says: "Alan's not strutting around trying to prove everyone wrong and himself right [like Sherlock].

"He's quietly working at changing things from a unique perspective of lateral thinking, but not then broadcasting it to the world in a swishy long coat to make policemen feel stupid."

Besides, he adds: "Alan's more into tweed. Sherlock has a bit of tweed going on, I suppose, with the deerstalker, but yeah, they are different."

A pioneering mathematician and computer scientist, Turing's part in cracking the German Enigma code at Bletchley Park went unrecognised in his lifetime.

In fact, his reputation and career were destroyed in 1952 by a conviction for homosexuality - or an act of "gross indecency" - which led to him accepting chemical castration as an alternative to imprisonment.

Two years later, aged 41, this tragic, unsung hero committed suicide.

There were no recordings of Turing available for Cumberbatch to watch when researching the character.

"It's a blank canvas to an extent, so you have a bit of freedom, but you have nothing to bounce off."

Instead, he met with people who had known Turing, to "personalise this extraordinary man whose achievements we know in broad headline terms".

One of those who formed a close bond with Turing was his one-time fiancee, Bletchley cryptanalyst Joan Clarke, portrayed in the film by Cumberbatch's Atonement co-star Keira Knightley.

Turing broke off the engagement after admitting his sexuality to Clarke, who died in 1996.

"He was someone who was caring and loving, as well as someone who was determined and often in isolation," says Cumberbatch, who believes the film will send out a positive message to the young.

"If any young person's ever felt like they aren't quite sure of who they are, or aren't allowed to express themselves the way they'd like to express themselves, if they've ever felt bullied by what they feel is the normal majority, or anything that makes them feel like an outsider, then this is definitely a film for them. It's about a hero for them."

The son of actors Timothy Carlton and Wanda Ventham, Cumberbatch didn't start performing until he boarded at Harrow School. He went on to study drama at Manchester University and Lamda (after taking a year out to teach English in Tibet) and soon began appearing on stage and in TV dramas.

After critically acclaimed performances in Amazing Grace, Atonement and Small Island, he made his Sherlock debut in 2010 and landed roles in The Hobbit trilogy and JJ Abrams' Star Trek Into Darkness.

He says he's learned to deal with the fame and constant attention by "normalising it as much as possible".

"But no, it's weird," he admits. "Some of it's really enjoyable, some of it's plain bizarre. But most of the bizarre stuff has been benign, so you kind of roll with it.

"What's great about where I'm at in life is the amount of extraordinary work I'm being offered. That's wonderful and not to be overrated in a profession that's woefully underemployed.

"I'm very, very grateful for the good stuff."

His upcoming starring role as Hamlet at the Barbican theatre was reportedly the fastest-selling ticket in London theatre history.

"It's a comfort, it means there's going to be somebody turn up to watch the work!" he says smiling.

"It's a great impetus to do a lot of work on it.

"Not that we hadn't already - it took us months to find the right venue and before that, there were a lot of conversations.

"It's exciting, I'm looking forward to it. But it's a year away, so that can exist for then."

In the meantime, he's clearly delighted to champion Turing and his achievements.

"Any aspiration I have for the film is just to broaden people's knowledge of him and get his story to a wider audience, so his legacy is truly celebrated the way it should be.

"Not just the tragedy of his suicide, and the reasons for that, but also his extraordinary brilliance and his life journey - this incredibly sensitive human being who was like touch paper to the world."