While I am failing to have breakfast with Benedict Cumberbatch in a Hampstead bakery that no longer exists — his suggested venue, but as you will see the boy has been busy — strangers are waiting in his flat around the corner. He found them on his doorstep and they were chilly, so he let them in; luckily, they are our photography team, or at least he hopes they are. “It’ll be all right, won’t it?” Of course it will. The world is beaming so warmly on the tall, rangy 34-year-old with his lovely cologne and Old Harrovian manners, that you could toast your fingers in the glow. While the rest of us lumber on, the actor is ice-skating in pirouettes, doing justice to his big moment by overtaxing his diary, accommodating everyone, surviving on little sleep. His updated Sherlock Holmes may have traded the pipe for nicotine patches, but with ratings for the BBC show passing 7m, the actor is lighting up and laughing about the filthy exchanges about him on Twitter. “It seems girls are really going for my Shergar look.”

The night before we met I had seen him at the Lyttelton Theatre in Terence Rattigan’s ecstatically reviewed play After the Dance. He was as brilliant as billed as the former bright young thing David Scott-Fowler, now trapped in the eternal cocktails and moral vacuum of the idle rich. He is weak and selfish, but imbued by Cumberbatch with such charisma you somehow understand his fatal attraction. After the show the actor had showered, danced around to Skeleton Boy by Friendly Fires to “shake off” the interwar years, and dived into the National’s Green Room to have a drink with his friends, but then escaped to the fresh air of a balcony, alone. “I just felt, ‘This is too much.’ I was hot. So I walked away from everyone.”

He rode home on his Honda CBF600 to the north London flat he shares with his girlfriend, the actor and writer Olivia Poulet (Emma Messinger in The Thick of It), but lay awake, his mind racing. He is dog-tired, keeps forgetting names of his fellow actors, can’t think of a show Olivia was in and berates himself for it; at one point he pours semi-skimmed over the back of his spoon into his coffee, then catches my puzzled look. “God! Look at me. It’s not even cream.”

The fatigue is fitting in such heady days. Two hours before his curtain call yesterday he had been to the Connaught hotel to meet a dapper, bearded director whose softly crooning voice he imitates brilliantly. This month Cumberbatch begins shooting on Steven Spielberg’s adaptation of War Horse, Michael Morpurgo’s story of the Devonshire farm horse taken to France in the first world war.

He plays Major Stewart, leading the doomed cavalry charges across the western front, in a script by Richard Curtis and Lee Hall. Initially required to read the script in a Soho office in cloak-and-dagger secrecy, when he was offered a drink he thought they were plying him with alcohol to see if he would give away a sneak peak.

“I thought there were hidden cameras, that it was some sort of test.” Two weeks later he was offered the role, and his plans for a holiday disappeared. “I had literally been joking that I planned to go away unless Steven Spielberg called... and he did.”

And if that weren’t enough, he has also just won the role of Peter Guillam, George Smiley’s MI6 protégé in the remake of Tinker, Tailor, Soldier, Spy by the Swedish director Tomas Alfredson, with Gary Oldman as Smiley. “War Horse is a thrill, and an incredible CV filler, and Spielberg is amazing... but to me this is...” More exciting? “God, don’t say that, it’s just that it is such a grown-up role.” And he still makes time to be a “human Ticketmaster”, spending an unbelievable hour and a half every day organising tickets for friends and family, starry mates like Rosamund Pike, and the parents of the guy who lives downstairs (seriously).

Cumberbatch is super-bright, perched on the edge of life-changing celebrity, after which the personal managers and LA publicists will take over.

Then he will never be able to let strangers know his postcode, let alone avail themselves of his tea bags. For now fame is still distant enough for him to show you his family pictures on his iPhone while he hoovers up bacon and eggs in Carluccio’s as if he hasn’t eaten a proper meal for a week.

He seems wired with the excitement of it all, rewarded for his abundant charm with the goodwill of everyone he meets — waitresses, dogs, his co-stars, the ancient eccentric with the pipe on Hampstead Heath who stands next to him for a photograph, my smitten seven-year-old who is in the back of the car when we drive to another cafe, whispering in a loud aside: “I think he’s Doctor Who.” Actually, contrary to rumours, he never turned down a shot at the Tardis because he was never offered it. “I’d turn it down anyway,” he says, of the series, written by Steven Moffat, one of the writers (with Mark Gatiss) on Sherlock. “Jumping onto school stages and giving out prizes and saying ‘I am the Doctor’, it’s not where I want to go.”

Somehow his work seems more tied to the elegant, elegiac past than the sci-fi future; his inspiration is the frightfully English Trevor Howard, whose clipped diction he studied for the upper-class David Scott-Fowler. Now for War Horse he’s been watching Howard’s doomed and heroic Lord Cardigan in The Charge of the Light Brigade. “I could not believe it was the same actor.”

For all these thrills, a part of him is also anticipating disaster. This is not innate pessimism, but the legacy of a violent carjacking he suffered in South Africa in 2004 while filming To the Ends of the Earth. He was beaten, bundled into the car boot and thought he would die. “I knew my mother was going to get a call either from me or someone else, and the difference would change her life.” Just before the tyre blew out, forcing them to stop, he had been listening to Radiohead, blissfully relaxed. “It was one of the best times in my life. Then bang. Every time I’m feeling really good, a bit of me is waiting for that bang.”

Benedict Timothy Carlton Cumberbatch is the adored only son of the actors Timothy Carlton (Lewis, Heartbeat, Foyle’s War) and Wanda Ventham (Cassandra’s mother in Only Fools and Horses), both still working, stalwarts of popular TV series and commercial theatre. As an embarrassed adolescent, he watched his glamorous mother making stage entrances and pulling a shocked expression as one actor pulled at another’s trousers, simulating oral sex, but actually trying to help him change before his girlfriend comes back. “I had to say to her, sorry, Mum, I just can’t bear to see that gag one more time.” He chuckles: “I was so sensitive to it, she must have wondered if I was gay.” Rather than pushing him into the family business, his parents hoped an expensive education might encourage him to get a proper job. “At 15, they kept saying, ‘Look at us, how out of control our lifestyle is, how money’s a huge ebb and flow.’”

His mother, whose contemporaries are Judi Dench and Diana Rigg, turned down Peter Brook’s invitation to the Royal Shakespeare Company because she was pregnant with her daughter from a previous marriage, and now her son worries about her missed opportunities. “I’d love her to have a ‘Cranford moment’, but for that you have to have a huge backlog of classical roles.” It is a mistake he doesn’t have to fear repeating.

After studying drama at Lamda and Manchester, his breakthrough was starring in BBC’s 2004 Hawking, in which his depiction of a brilliant mind and failing body won him a Bafta nomination. He got a reputation for being intelligent enough to play geniuses, Van Gogh, Pitt the Younger in Amazing Grace, and now his borderline Asperger’s Sherlock Holmes. There was another Bafta nomination for his bigoted landlord in Small Island, and even his early Love’s Labour’s Lost at Regent’s Park saw him shortlisted for an Ian Charleson award. His rise has looked easy, and you guess he wouldn’t be acting at all if it weren’t. He is assiduous — learning violin for Sherlock, becoming an adept rider for War Horse — but not a slogger, or remotely earnest.

As a child he describes himself as a “hyperactive nightmare”. The headmaster at Brambletye, his prep school in East Grinstead, realised he needed structure and responsibility, and suggested his old school Harrow to the Cumberbatches. “It suited me down to the ground. I was gregarious and found a coterie of brothers I’d never had before. I fell in love with the place.”

It was also, of course, the alma mater of Terence Rattigan, and in his first big role he played the pitiable classics master Arthur Crocker-Harris in The Browning Version. He was in the playwright’s old house, read the same books in the Vaughan Library, studied the same Greek translations, and with “Ratt Soc”, visited London’s theatres. Unlike some of his friends, it wasn’t just for the “cheeky drink and a smoke” in the interval. He remembers seeing The Deep Blue Sea with Penelope Wilton at the Almeida. “It was mind-blowing for me. The big moment. I realised Rattigan had a profound depth. It’s the same with Coward. Among all the wit, when the mask slips it’s painfully raw.” When first offered After the Dance by the director Thea Sharrock, he was unsure, however, feeling he was almost “too right” for the part and fearing some unhealthy reversion to type, but then he couldn’t resist.

He chose Manchester, where he met Olivia Poulet, for its lack of drawing rooms and silver spoons, and it was there, in Mamet’s Glengarry Glen Ross, that he broke his father’s heart with pride. “After the show he told me I was a better actor than he had ever been or would ever be. He was tearing up as he was saying it.” He has continued to be “terribly proud and utterly selfless”, revelling in his son’s success. When Hawking was well reviewed in The Sunday Times his father framed the drawing that accompanied the piece as a 28th birthday present. “Mum gets a bit emotional on first nights,” he says, “but Dad... he started to weep at the first night of After the Dance when he was telling me how proud he was. I didn’t know what to do. I just held onto him. I said, ‘You’re not crying out of relief that I got through it, are you?’ And he said, ‘No, you stupid boy. I’m crying because you were so wonderful.’”

Cumberbatch — he flirted with changing his name to Carlton like his father, but soon realised there was no need — is not one of the pretty boys. His looks are too striking and unusual to make him the sort of rom-com pin-up who opens a movie. He has exotic cheekbones, slanting blue-green eyes (“mum’s”), retroussé nose (“my aunt’s”), thick hair (“dad’s”), and the most lavishly accentuated upper lip since Clara Bow. Look closer and its outline seems to have been tattooed, making his cupid’s bow visible from halfway back in the stalls. The marking first appeared when he was working in South Africa, skin damage, he was told by a dermatologist, and an indication of high oestrogen levels normally seen in men with cancer. He was tested and cleared. He laughs: “Then I was just worried that people would think I wore make-up every day.”

The looks, which lend Holmes his effete aura and ambiguous sexuality, are helpful for a character actor, chameleon enough to see him play a twisted killer or a flouncing Kenneth Williams. “I’m aware of the power of looks,” he says. “I’ve wanted to play roles that have gone to much better-looking people and you just think, ‘Oh well, that’s the pin-up guy’s… an actor like my friend James McAvoy, who’s gorgeous on screen. I’m not that. But at least I don’t have to worry about taking precious care of my face because it’s my commodity. That’s a great freedom. I’m not afraid of being heinous for the sake of a part.”

He was recently compared in The Mirror to Shergar, but finds the insult hilarious, claiming to be flattered. “The irritating thing is that I’ve always said that myself, and now some journalist has taken credit for it. I looked good in the picture, the horse looked good. What’s the problem?” At the press launch of Sherlock he was asked if he minded being typecast as intense, clever, sexually ambiguous characters and, feeling relaxed, he risked a joke. “I’m here to tell you,” he announced, “that in real life I’m a f***ing fantastic lover!” He groans. “That got everywhere. Everyone was coming up to me going, ‘So, how good are you, exactly?’ Jesus Christ…”

Actually, he is keen to flex his alpha-male credentials in Atonement, After the Dance, now War Horse. “I’d love to beef up and do a Tom Hardy [the star of Bronson]. Bring it on.”

The starring roles in War Horse, the story of a young boy who tries to find his horse Joey in the trenches of France, really belong to the stallions, who for the first time ride into the tanks, guns and gas of war. In real life, the lead is a 17½-hand equine gladiator, “half a tonne of 35-miles-per-hour joy” as Cumberbatch puts it. “It’s not told from his perspective like the book, otherwise it would be Disney, but obviously the Bafta will go to Joey as best horse actor.”

Horror of horrors, he was late for his appointment with Spielberg because of Westminster’s frustrating parking system, and the director’s clipboard minions were twitchy when he arrived. “So I went in with my shoulders up saying, ‘Sorry, so sorry,’ and Steven was just so sweet. I told him that the officers mustn’t look like doomed upper-class fools, there has to be something heroic about their charge, and he agreed.” Accompanying Cumberbatch at the audience were his equally nervous fellow officers Tom Hiddleston and Patrick Kennedy, also public schoolboys, the latter at Harrow where he played the son Biff to Cumberbatch’s Willy in Death of a Salesman. “We were together in Atonement as well. Steven was saying, ‘My God, you guys, you are like a club, you’re so unbelievably perfect for this, it’s great.’ But we are really vehicles for the horses, it’s their journey.” He laughs. “Tom was going into character, and Steven was saying, ‘Yeah, all that’s great, but we gotta get the right horse.’”

Until schooling began for the film, Cumberbatch hadn’t ridden since he was 12, but at a riding school near Harefield, full of actors on horses, he is winning over his horse, Topthorn, whose real name is Faldo, a former dressage star. “The trust forms through proximity, giving him his hay bag, washing him down, being close and touching. He’s so calm he starts falling asleep on my sleeve.” Recently they were all lined up for group charging practice in a nearby field, single file, then double, then in rows of four. There were 10 of them, but on the day the scene is shot there will be 80, increased by CGI to a rumoured 300. “Ten is enough, though. Being in a line of 10 horses on a controlled canter, getting out your sabre, and looking down the line, it’s just extraordinary.”

Stunt doubles will be used for most dangerous equestrian sequences. “They have to. You can’t insure actors to do it. When I hear Daniel Craig and everyone talking about doing their own stunts I think it’s bullshit.” Yesterday Faldo reared twice, having been given contradictory commands by his novice rider. “I quite liked it. I have a high danger threshold. People were shouting ‘the reins, drop the reins’, because the more you pull the more they rear, but you can’t hear properly as you turn. Afterwards Tom and Patrick were so public school about it, going, ‘Wow! That was so cool.’”

As the beneficiary of such a privileged, warm, solid background (a pretty good advert for boarding school), Cumberbatch might be accused of lacking edge, but he seems to have frailties, susceptibilities, a vulnerability from pushing himself hard. “It’s not that I get ill when I’m under stress,” he promises. “If that was the case I’d be on a drip in hospital right now.” But I’m not sure I believe him. At Manchester he had the overworker’s disease glandular fever.

While he was performing in Rhinoceros and the Arsonists at the Royal Court in 2007 he developed a stomach ulcer. He fell ill while filming Sherlock in various freezing Welsh locations, including a perfectly Gothic old railway tunnel in Barry, dripping with damp and full of smoke and soot from the braziers.

Despite his swimming and daily dose of honey and Bikram yoga — “to keep angular and interesting for Holmes” — his flu turned to a pneumonia that nearly led to hospitalisation. “It was because I was throwing myself into it with no rest, I was in utter denial, having too much fun because I love the character so much. Basil Rathbone and Jeremy Brett may be the ideal Victorian heroes, but I want to be the modern one.” As for Robert Downey Jr in Guy Ritchie’s version (with a sequel on the way), he is unperturbed by the competition. “He’s great, but that’s not Holmes, it’s Robert Downey Jr.”

His future looks tightly mapped, but he badly wants to be a father, saying he intends to take more control over his life next year to make space for a family, a plan I have never before heard from a man. He and Olivia split up for a few years, but have been back together for four, the past two sharing their bohemian idyll with its teeny kitchen and wonderful roof terrace — “my sanctuary” — where they drink wine and listen to the church bells and the swallows and swifts screeching over their heads. “I don’t know if we’ll get married. We both want children, but not necessarily right now, and not necessarily with each other. We’re great as we are for now.” Is there one role he dreams of, Hamlet, for instance? “Yes, but it’s been inflicted on audiences too much. There’s been Stephen Dillane’s, David Tennant’s, Jude Law’s, Ben Whishaw’s, Rory Kinnear’s now, Michael Sheen’s doing his as well. I mean, f***ing Jasper Carrott will be doing it next! It’s like there’s a queue. I think we’re just seeing people do their Hamlet, that’s where it goes wrong. I’m more interested in Edward II at the moment.”

Meanwhile there are stallions to master, hair colour to adjust for Steven (“he just wants to take it down a few shades”), and an almost poignant letting go of his young meteor status to embrace the “grown-up” life he seems to crave. Last week two school friends came to see his play, and he had hugged them close afterwards, comforting himself as much as greeting them. “They were an anchor of reality,” he says. To what? “To what I was and what I will be again when this crazy time in my life has passed.” Maybe.