Fans are hanging out of the windows of the buildings bordering 221B Baker Street. On the other side of the road, by Euston Station in London, thousands more aficionados are penned in behind temporary metal fences. 

As their hero strides into view, wearing his trademark Belstaff “Milford” coat, the crowd – vast numbers of whom have travelled from China and Japan and slept here overnight specifically for this very moment – start screaming. Very soon they are doing a pretty passable impersonation of Justin Bieber followers, or “Beliebers”, as they are known in the trade. By this point, people in neighbouring counties will surely have heard the news: Sherlock is in town.

Benedict Cumberbatch, who plays Sherlock Holmes in BBC1’s global hit drama, has arrived to film a short exterior scene outside the consulting detective’s flat. The sleuth must march to his front door through a monsoon, the ferocity of which has probably not been seen this side of The Tempest. The downpour is being created by three gigantic rain machines. The poor crewmember holding these enormous devices steady must have the worst job in showbiz. 

You might have thought that these decidedly inclement conditions would pour cold water on the fans’ enthusiasm. But in fact the crowd seems to thrive on the spirit of adversity. Sherlockians are nothing if not determined. The wetter they get, the more they cheer. Absolutely nothing is going to rain on their parade. 

Before his storm scene, Cumberbatch sits in the warm and dry of a nearby hotel. He is taking time out to discuss the new series of Sherlock, perhaps the most eagerly anticipated event since the birth of the last royal baby.

To reinforce the global popularity of the show, which begins its fourth series on New Year’s Day, our chat is interrupted by a Japanese fan eager to present the actor with a gift: a beautifully produced graphic novel based on a previous episode of Sherlock. Cumberbatch is bowled over by the exquisite nature of the present, which has clearly required many months’ work. “Thank you very much, Japan!” the actor beams. “I’ve got to read this backwards. Wonderful. Wonderful. Thank you.”

In person, Cumberbatch has nothing of Sherlock’s outsider quality. The actor is as warm, witty and welcoming as his alter ego is detached, difficult and dry as dust. 

Sherlock Holmes is the literary character who has been most frequently adapted for the screen. Since he first appeared in A Study in Scarlet in 1887, it is estimated that across the globe there have been more than 25,000 productions and products based on Sir Arthur Conan Doyle’s timeless detective.

But Cumberbatch’s performance as the sleuth now bears comparison with Jeremy Brett, Basil Rathbone and Peter Cushing. When His Last Vow, the final episode of the third series, aired in January 2014, it shattered the world record by prompting 10,000 tweets per minute.

With his angular features, piercing intelligence and rare intensity, 40-year-old Cumberbatch could have been born for the role of Sherlock. But his performance is enhanced by the magnetic chemistry he generates on screen with Martin Freeman, who plays Sherlock’s long-suffering friend and colleague, Dr John Watson.   

Mark Gatiss, who co-created the show with Steven Moffat, says that the drama “works so well in our version because of the casting. When Benedict and Martin first read for the parts of Sherlock and John, Steven and I turned to each other and said, ‘There’s the show.’ We accidentally cast the two hottest actors in the world.” 

Amanda Abbington, who portrays Mary Watson and is Freeman’s partner on and off screen, agrees. “I love a big dialogue scene where characters are getting under the skin of people, and I think that Ben and Martin do that with each other. They just naturally have that on set and on screen – they just get on. It’s lovely to watch. It’s great to be in a room when you see them with those long deduction scenes and they’re bouncing back and forth. It’s beautiful.”

That chemistry is again in evidence in the opening episode of the new series, The Six Thatchers. Written by Mark Gatiss, the drama follows on from the end of the last series, when Sherlock declared that, “Moriarty is dead. More importantly, I know exactly what he’s going to do next…”

As the sleuth waits to find out what Moriarty’s (Andrew Scott) posthumous move might be, Scotland Yard tackles a particularly bewildering case. But Sherlock hones in on an apparently trivial detail. Why is someone desecrating images of former prime minister Margaret Thatcher? Are dark forces operating? And is it connected to Mary’s mysterious past?

During the series, the sleuthing duo have to factor a new element into their relationship: John and Mary’s baby daughter, who leaves Sherlock quite baffled. The pair will also be confronted by Culverton Smith (Toby Jones), who is the dastardly poisoner in the Doyle story The Adventure of the Dying Detective. Moffat describes him as “the most evil villain we’ve had”. So we can safely assume that something wicked this way comes.   

Sherlock, which has won 76 awards since it was first transmitted in 2010, now airs in 240 territories across the world. Cumberbatch, who is married to theatre director Sophie Hunter and has a young son and another baby due next year, assesses why the show has struck such a chord internationally.

“I think a lot of it is to do with the fact that Sherlock is an outsider, and that speaks to a huge teen audience. But remarkably it also has tremendous cross-generational appeal. That’s very important to me. I want my mum and dad and my friends and my child to sit down and watch it. That’s what really gives me a thrill, that moment of the event. 

“I think that happens wherever it’s broadcast. It’s created huge forums and debates and friends around the world, and that’s a lovely thing. Word of mouth spreads very fast with blogs and Twitter and Tumblr and all the other social media platforms where audiences share their opinions.”

All the same, the sheer scale of Sherlock’s global popularity has taken Cumberbatch aback. “We’ve been shocked by that, to be honest. It’s something that we did not foresee. But in the end, it shows that great stories traverse cultures and ethnicities and nations. Great stories bridge any kind of cultural differences.”  

Cumberbatch has plenty of other filmic fish to fry. Earlier this year, he was Richard III in BBC2’s acclaimed Shakespeare adaptation, The Hollow Crown. He also played the title character in the new Marvel movie franchise, Doctor Strange.

And yet he keeps being drawn back to Sherlock. Part of the attraction, Cumberbatch explains, is that the character is always changing: “We’ve all evolved with this story. It wouldn’t be so satisfying if we were simply churning out the same thing that we started with. We aimed high to begin with, and we keep on trying to surprise ourselves and hopefully our audience.

“There are payoffs in this series that I know in some instances even the writers didn’t realise were happening until they were starting to write it, which is just remarkable. The level of invention and imagination and darkness and joy just gets better and better.

“There’s a lot of very serious stuff, and it’s very bleak at times. But the writers also manage to do something very funny as well. How do I feel personally about that? Great. And, you know, I wouldn’t be coming back to do more if there wasn’t a difference between this series and the first series. I’m very lucky to have a character like this, who I still really want to play.” 

That’s not to say that he’s unaffected by the role. He admits, “There is a kickback. I do get affected by it. There’s a sense of being impatient. My mum says I’m much curter with her when I’m filming Sherlock.” 

However, in general Cumberbatch does not take Sherlock home with him in a hansom cab. How does he do that? “Obviously exercise is a very important thing, just to shake anything off. If you run or do something to get a sweat or a burn on, then yes, that helps hugely.”

But there is one aspect of his life above all others that helps Cumberbatch forget about the stresses and strains of playing the world’s most famous detective. “Having a one-year-old baby is just the best possible tonic to go, ‘Boop!’ You know, with a baby you’re instantly looking outside of yourself.”

Displaying a distinctly un-Sherlockian love of babies, Cumberbatch says, “Immediately there’s something more important than you’ll ever be in your life that you’re responsible for. Home is a very wonderful place!”   

The fourth series of Sherlock begins tonight at 8.30pm on BBC1