Hero of Baker Street returns... and has he got news for you

He's fought off Moriarty, wowed theatre audiences and turned in some nifty film cameos, but Benedict Cumberbatch is terrified of his next role. This time he will have to improvise, thinking on his feet alongside a formidable line-up and in front of a vast and demanding audience.

On Wednesday, he will record Have I Got News For You for the first time, the first of the 10-week series' guest hosts. The next evening, the nation will see how he fared: "From people I know who have done it before, it is really good fun," he says, "however heavy the laundry day may have to be the next morning...."

If he considered turning down the show, it was not for long. "It's really an honour for my father and mother as we used to watch it together; though I imagine Paul [Merton] will come up with the idea that he doesn't know who I am."

The thought of the coming ordeal would make anyone jumpy. On top of which, he and writer Stephen Moffat have been grilled – ahead of their show's US debut – about this year's reboot of Sherlock. So I'm prepared to forgive him a little tetchiness as he wraps the interview before mine, with American television.

For 34-year-old Cumberbatch, though, it has been a breakthrough role. In only three episodes, it captured the public imagination – nine million viewers – and established him as a leading man. Another series is on the way in the autumn of 2011. "There is so much love for it. It really bowls you over, the kind and variety of people who love it and are eager for more."

The love comes at a price. The six foot-something Cumberbatch who leaves Bush House for the Waldorf hotel slips unoticed past fans by sporting blonde, curly locks, clomping-great biker boots and a leather jacket. He could hardly appear more different from his TV Holmes, whose tweedy style triggered a fashion revival.

There is a noticeable brashness, a confident intensity to Cumberbatch. On paper at least, he is almost a parody of a public schoolboy – he went to Harrow and loved it. He threw himself into paragliding, abseiling and drama, which he went on to study at Manchester University. Despite the privileged education, he has a reputation for working hard and with a purpose. At university he overdid it and contracted glandular fever .

Both of his parents are actors. His father Timothy Carlton (his stage name) Cumberbatch has been appearing in television roles since the mid-60s. His mother, Wanda Ventham has appeared in everything from The Saint with Roger Moore to Only Fools and Horses. But neither has had the high profile their son now enjoys.

You could dislike this man who has it all, but he fends this off by playing down the the whole public school, actor schtick. Asked if he was inspired by his parents, he avoids the traditional, grateful gush: "Yes, and no. Because I saw the working practices behind what they did, it didn't carry a lot of mystique. I knew about the peripatetic nature, the uncertain income what it can do to your social life – all of that. I actually initially wanted to be a barrister."

His frankness is disarming; his confidence seems founded on thought and experience rather than learned on the playing fields of privilege or amid midnight feasts in the dorm.

If he does seem a little more than averagely contented with his lot, he is probably entitled to. He has plied his trade for the best part of the past decade, winning small parts in big films: nerdy Patrick Watts alongside James McAvoy in Starter for 10; confectionery magnate Paul Marshall in Atonement. And, he insists quietly, he has paid his dues: "I've kind of struggled to get to that. I'm enjoying playing Holmes but he's funny as well. But when you're the butt of the joke, always playing the fool, that can be tiresome. I've gone from playing Patrick in Starter for 10, to Major Jimmy Stewart, to playing the lead role of David Scott-Fowler in After the Dance."

Larger roles in smaller productions brought him critical acclaim: 2004's Hawking where he played the young physicist, and as the author Alexander Masters in the affecting Stuart: A Life Backwards, the true story of a mentally unstable boy who becomes homeless and who is befriended by Masters.

Besides working on new theatre, television and film roles – he is currently filming Stephen Spielberg's adaptation of War Horse and John le Carré's Tinker, Taylor, Soldier, Spy. It has been a good year.

With fame has come recognition. "Even though my hair's a different colour, people do still recognise me. That has happened, which is odd.... It's mainly positive, but you do get a few spiky people who want to have a go, but I can just about deal with them: I've got the energy for it. It might be different if I was older."

There, again, is the mix of confidence and candour. He has no hesitation in lambasting the current coalition government when it comes to effect proposed cuts will have on the arts: "People are going to be shocked at how it will affect the volume of output and choice that they're very used to at the moment. The arts provide a massive return of revenue, employment and hold national prestige.

"There are five people at the Royal Court who earn around £140,000 collectively and bring in around £1m per year: that would get you a big bonus in the City. I'm interested in art for all. I don't want it to be only the sons and daughters of Tory MPs who get to see my plays."

There are areas where the shutters slam down – his relationship with his partner, an actress – and his private life generally. Talk of his being the next Dr Who is another no-go area. "Everyone talks about Dr Who as if it's something to aim for, but I'm very happy being Sherlock Holmes. I'd much rather surprise people with what they might like, rather than what they already know they like."

I suspect he'll be able to hold his own with Paul Merton.