If you stop Benedict Cumberbatch on the street and ask him, “Aren’t you Sherlock?” brace yourself: When it comes to his role as the scarf-flinging, long-coat wearing crime-solver in the contemporary British version of Arthur Conan Doyle’s Victorian-era detective story, Cumberbatch is a gung-ho, one-man marketing team.

“I go, ‘Yeah, I am. Now tell me: How did you see ‘Sherlock’? When did you see it?” Cumberbatch says. He hopes that when the second season of “Sherlock” begins May 6 on “PBS Masterpiece Mystery!” it will spark the same sort of national obsession as it did when it ran in England.

“That’s the most smug thing I feel about all [the success of “Sherlock”] — that it’s people with brains, with sophisticated tastes, who really enjoy this,” he says. Sherlock geeks pore over ever detail as he and Dr. Watson (Martin Freeman) solve crimes. “They really like the complexities of the character. They follow the humor.”

Lately, Cumberbatch has had plenty of opportunities to wage his “Sherlock” campaign. For the past five months, the 35-year-old Londoner has been living in a 3-bedroom storybook cottage in Venice, Calif., only a 10- minute drive — in a borrowed silver Jaguar — from Sony Studios where he’s currently filming his first mega-budget Hollywood movie — J.J. Abrams’ untitled “Star Trek” sequel.

Has strolling around the same lot where “The Wizard of Oz” was shot lived up to his Technicolor expectations?

“It’s amazing,” Cumberbatch says. “First an Egyptian walks by, then Lady Gaga, then somebody going to a game show.”

He’s so worried about divulging too much about his role as the villain in the top-secret movie that he cuts himself off mid-sentence about walking into the makeup trailer and finding a co-star being transformed into pointy-eared Vulcan or maybe a Klingon.

What he can’t hide, though, is that Abrams obviously wanted a more ripped version of Cumberbatch than the one who plays the thin, pale Sherlock.

“I’m on a fitness regime,” he says while sitting at a long, wooden table in his kitchen in faded black jeans, black sandals and a gray T-shirt from which new biceps bulge. “I’d be very wary — especially of the white ones,” he jokes when after devouring a large breakfast of scrambled eggs, lox and buttered toast he swallows the contents of a baggie of white-and-orange vitamins.

As for the long, foppish black hair extensions he’s wearing to play a “Star Trek” baddie, he’s self-conscious about them. “These gleaming bits of plastic sitting on my skull,” he says ruefully. “People probably look at me and think, ‘Oh, bless him. He’s got bits of food in his hair that he doesn’t know about.’ ”

Before “Sherlock” and “Star Trek” and the silver jaguar, Cumberbatch, who trained at the London Academy of Music and Dramatic Art, toiled in the trenches of film, TV, theater and radio playing slump-shouldered losers (“Fortysomething”) and germphobic neurotics (“The Last Enemy”).

“He was always a weirdo elder brother or the rapist,” says “Sherlock” co-creator Steven Moffat, who knew the minute that he met Cumberbatch that he’d found his dashing oddball of a leading man. “[Benedict] will go on and do lots of magnificent things but people will always remember ‘Sherlock Holmes.’ It’s a glorious bit of casting, one of those great moments — like when Connery played Bond. This is his hero role. It’s the part that made him sexy.”

When asked about his sex appeal, Cumberbatch gets a nervous look on his face. “I look at photographs, the ones that people ask me to sign sometimes, and think, ‘What are people seeing?’ I have had this face for 35 years. I’m never going to change it. But I wouldn’t desire me. I can see beauty in other men. Ryan Gosling? F- – k. George Clooney? Wow. But you can see the enigma in those kind of faces. But I can’t see it in myself at all.”

If you asked his actor parents — Timothy Carlton (nee Cumberbatch) and Wanda Ventham — they’d probably tell you that their only child’s road to unconventional stardom began at age 3 when he headlined as Joseph in a nursery school Christmas play.

“Mary was taking a hell of a long time with her lines so I pushed her out of the way,” says Cumberbatch. “All the parents were laughing but Mum and Dad were mortified.”

Hollywood has noticed his high cheekbones, distinctively feline eyes and dramatic versatility. Last year, Cumberbatch excelled with small but memorable parts in “Tinker Tailor Soldier Spy” and “War Horse.” Director Peter Jackson cast Cumberbatch in two high-profile parts in his fantasy epic, “The Hobbit: There and Back Again”: he’s the voice of the necromancer and a talking dragon.

Acting for Peter Jackson is just the latest bit of Cumberbatch’s good news. In mid-April, he and Jonny Lee Miller won a shared Best Actor Olivier award for their performances in the Danny Boyle-directed stage version of “Frankenstein.”

Cumberbatch and Miller alternated playing Victor Frankenstein and his scar-faced monster.

“Frankenstein” won’t be the last time he and Miller will play the same part. CBS has been so eager to capitalize on the success of “Sherlock” that they’ve cast Miller in the fall pilot “Elementary,” an updated US-based version of Conan Doyle’s super sleuth, but with a sexy gimmick: Lucy Liu will play a female Dr. Watson.

When asked about “Elementary,” Cumberbatch says, “[Jonny] is my friend and I wish him the best of luck.” But he won’t pretend that the rival show doesn’t stir protective feelings. “What I’d like is for it to be acknowledged that we did originate the idea of modernizing Sherlock Holmes in the 21st century,” he says.

What he fears the most isn’t being bested in the dialogue department — “I would be amazed if they have as consistent a quality of writing as we have on our series,” he says — but a network’s ability to launch a wall-to-wall marketing campaign.

“I’d be sad if ours was crowded out by huge posters on Sunset Boulevard. As much as I’d love it, you don’t see billboards [for our ‘Sherlock’] on the side of the HBO building. I’d love to go to Soho House one night and go, ‘Oh look, there I am with Martin.’ That would be great.”

SHERLOCK: A SCANDAL IN BELGRAVIA

Today, 9 p.m., PBS