He was born in London, to parents who were in the business — the actors Wanda Ventham and Timothy Carlton — and had his first substantial part in high school at Harrow, the famous boys’ boarding school that is the Yale to Eton’s Harvard. “I played the queen of the fairies,” he said. (That would be Titania in “A Midsummer Night’s Dream.”) Later, when he performed in “As You Like It,” an old alumnus watching the play apparently pronounced him “the best Rosalind since Vanessa Redgrave.” He went to the University of Manchester and the London Academy of Music and Dramatic Art, and then slid pretty easily into work; so far he has appeared in more than 30 films and dozens of television, radio and theater productions. But it was his title performance in “Sherlock,” which debuted in 2010, that propelled him to a new league. Part of it has to do with the witty, knowing script, with its clever allusions to the old stories; and part of it has to do with Cumberbatch’s sublime portrayal of the odd, brilliant, infuriating, charismatic detective. Sherlock-the-character has a fanatic following, with fans who debate every Cumberbatchian movement and every plot twist with the fervor of grassy-knoll conspiracy buffs. Cumberbatch takes care to remind them that though they might well love Sherlock, Sherlock would never love them back. “I always make it clear that people who become obsessed with him or the idea of him — he’d destroy you,” Cumberbatch said cheerfully. “He is an absolute bastard.”

Over a follow-up breakfast at the Algonquin Hotel in New York a few weeks later, I started to see what his public life is like. We walked there after a quick trip to my office, in which we spoke to no one but which precipitated three breathless “Is that who I think it is?” emails from normally phlegmatic colleagues in under five minutes. (He came back a couple of weeks later, and the non-phlegmatic people were gaping in the halls.) In the street we had to move quickly, because crowds form if Cumberbatch stands still for too long. In the hotel, we positioned ourselves behind a pillar, but people spotted him anyway (when they asked for autographs, they invariably asked on behalf of their teenage children).

As good a sport as Cumberbatch is, he sometimes finds it a bit too much. Filming “Sherlock” last year in Cardiff, Wales, he had an awkward interlude when he had to walk from his trailer to his car wearing a costume that, had anyone seen it, might have become a major plot spoiler. When he failed in his efforts to get a particularly persistent paparazzo not to photograph him, Cumberbatch shrouded himself in a hoodie (“I looked like Kenny in ‘South Park’”) and held up a sign he had hastily fashioned that said: “Go photograph Egypt and show the world something important.” The move was lampooned by the British newspapers, particularly when, to the delight of hundreds of fans massed on the street in London for another shoot, Cumberbatch did it again, this time with signs printed with provocative questions about democracy, government intrusion, journalism and the battle between liberty and security in the war on terror. “These are very complex questions and very difficult arguments to be very clear about, so to ask the questions is to stimulate the debate,” he explained. He has not done it since, though, he said, “I felt really strongly about it at the time.”

In New York he was visiting his friend Zachary Quinto, who acted alongside him in “Star Trek,” seeing some movies, going to some museums and trying to keep a low profile. He is currently unattached, and is gearing up for his next batch of work. One question that has excited “Star Trek” fans is whether his character, who all but stole the last film, will appear in the next one. There is certainly that possibility: He ended the film frozen in a pod and stored away in space. (“That was a stupid thing to do,” Cumberbatch said, referring to Starfleet Command. “They should have just blown me up.”) He pulled a cap over his head and prepared again to withstand the public. He says he has a way of negotiating big-city crowds: “If you pick a point far behind them they perceive you as not seeing them, and you’re the obstacle they have to get around.” For a moment, he sounded positively Sherlockian. “There is a way of just shadowing through,” he continued. “The higher the walls, the more dark the windows, the bigger the sunglasses — the more people are going to look. The greatest disguise is learning how to be invisible in plain sight.”