Benedict Cumberbatch puts celebrity to use illuminating historical wrong in 'The Imitation Game' 

Black Bear Pictures Benedict Cumberbatch as Alan Turing in \'The Imitation Game.\'

Benedict Cumberbatch broke the hearts of female fans around the world when he went public with his engagement earlier this month.

“Cumberbitches,” as they call themselves, clogged the Internet with laments after the British actor placed a sweet, old-fashioned announcement in his hometown paper, the London Times, that he’s marrying longtime girlfriend Sophie Hunter. (Or so he heard, because he steers clear of social media.)

But as uncomfortable as Cumberbatch is with having women he’s never met profess their undying love, he doesn’t mind the attention.

“I think most of it is good-natured and like anyone who’s ever been in the public eye and kind of revered in a way that I’ve been by these fans, the possession only takes on a sinister quality if the [fan] is really not very secure,” the 38-year-old actor tells The News.

“And since the woman I’m engaged to is as much a part of me as anything else in my life, if they like me, by extension they like her.”

The fame that’s come since his career-making role as the titular detective in BBC’s “Sherlock” and the flood of movies that followed — including “Star Trek Into Darkness,” “The Fifth Estate,” the Best Picture-winning “12 Years a Slave” and the upcoming “The Hobbit: The Battle of Five Armies” — makes for a big soapbox.

And that’s given him the chance to use his celebrity to bring attention to a historical wrong with his latest film, “The Imitation Game,” opening Friday.

Cumberbatch plays Alan Turing, the unheralded British mathematician who cracked the Nazis’ Enigma machine code during World War II, only to commit suicide in 1954 after being outed as a homosexual.

Evan Agostini/Invision/AP Cumberbatch and his fiancee Sophie Hunter attend the New York premiere of \'The Imitation Game\' at Ziegfeld Theatre last week.

Of all the parts Cumberbatch has taken in the past few years, none may be more personal to him than this — and not because of the buzz that the performance may net his own Academy Award nomination.

“I never dry in my enthusiasm in talking about playing this man or this film, no matter how jetlagged I am, no matter how repetitive it feels, or caught in the bubble (of hearing) your own voice,” Cumberbatch says of the period drama co-starring Keira Knightley.

“I feel like it’s part of our mission to broaden the audience of this man’s story and bring him to a wider public, because of his importance and because of how woefully treated he was in his life.”

Cumberbatch has long been a fierce advocate for equal rights — he officiated friends’ same-sex marriage last year in Ibiza — and got outraged just reading Graham Moore’s script for the first time.

Turing should have been hailed as a hero for his code cracking that helped the Allies defeat the Nazis. Instead, he killed himself at age 41, after being convicted of “gross indecency” for admitting he had a sexual relationship with a man at a time when homosexual acts were considered criminal in the U.K.

Many of Turing’s fellow Brits were unaware of his integral role in the Allies’ victory until a posthumous pardon from the Queen last year that came six decades too late.

“Part of the injustice that people get furious about when they watch this film and are moved by, [is] not just his demise and how shameful it was, but why he wasn’t well known,” says Cumberbatch.

“It’s one of the magnifications of the true tragedy of this man’s life. He should be on bank notes in the UK; he should be held in line with Darwin and Newton as a scientific pioneer. Why isn\'t he?”

Jack English Turing, the man who led the successful operation to crack the Nazi Enigma code, was prosecuted for his homosexuality and only pardoned recently by the Queen.

So Cumberbatch threw himself into the role with the same passion that he did when he traipsed around in a tight gray Lycra performance capture suit on the set of “The Hobbit: The Battle of Five Armies” to make a convincing giant dragon.

For “Imitation Game,” he had access to some of Turing’s surviving colleagues and nieces and took full advantage, spending hours in front of them perfecting which consonants to struggle with for the late scientist’s stammer.

“His nieces said it was like he was here again, which is wonderful to hear,” says Cumberbatch. “There is that weight of responsibility to get it right.”

Cumberbatch gets a rave review from “Imitation Game” director Morten Tyldum, who says the actor was his only choice to play Turing from the first time he read the script.

MIKE BLAKE/REUTERS Cumberbatch photobombs U2 at the 86th Academy Awards in March.

“The biggest problem with Benedict is you want to linger on his face while other people are talking,” says Tyldum. “Because his reaction to what’s being said and what’s happening in the scene is so interesting, it’s almost painful to cut away from him.”

The same can be said for Cumberbatch, who admits that the last few years have been filled with “pinch me moments.”

Such as sitting in his hometown’s most preeminent movie palace, London’s Odeon Leicester Square, flanked by his parents, veteran actors themselves, at the premiere for “The Imitation Game.”

“That was extraordinary and surreal, just as it was turning up at the airport with 1,000 Japanese fans waiting when I went to promote ‘Star Trek Into Darkness’ there,” Cumberbatch says.

Cumberbatch has deduced that a lot of new fans discovered him through \'Sherlock.\'

Cumberbatch uses performance capture to put some fire into his dragon in \'The Hobbit\' movies.

Or being on stage at the end of the Academy Awards last February as part of the ensemble cast for the Best Picture winner.

“Photo-bombing U2 (at the Oscars) was also surreal, but something that felt right at the time,” he adds. “And then only afterwards, I’d think, ‘Oh God, I’ve done that in front of the whole world,’ when I actually did it for one friend who kept on haranguing me for a photo with U2.”

It may be uncomfortable for Cumberbatch to admit, but he’s now a full-fledged celebrity, with all the scrutiny that comes with it.

That’s why the newspaper wedding announcement was so important for the self-proclaimed “old soul.”

“There are other operations in newspapers that find things out or try to publicize rumor and gossip,” he says. “I wanted to take control over the facts of it and announce it in a way that I would’ve done if I wasn’t famous.”

Imagine how rough it will get if, as rumored, Cumberbatch signs on to play Dr. Strange for Marvel. (He dodged a question about the role.)

“Fame is a projection of self beyond the work, which can be toxic,” explains Cumberbatch. “It can make you neurotic about your appearance, the perception people have of you, the lack of control you have over that perception.

“But fame is kind of what I’m paid for now, I fear.”

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