But then Henry's recent career changes tell their own story about someone who may be about to put his larger-than-life comic persona behind him and replace it with something quieter, more serious, and altogether less attention-seeking. He is keen to branch out from pure Light Entertainment. As Billy Connolly, Jack Dee, Robbie Coltrane, Eddie Izzard and others have discovered, an intelligent performer cannot live by comedy alone.
Henry and I are sitting in one of those hi-tech offices - all chrome and venetian blinds - beloved of advertisers. He is picking at a bowl of fruit. He is a huge man - a broad-shouldered 6ft 4in - with a huge presence. He has an aura that draws people to him - like one of those primitive force fields in an early episode of Star Trek.
Henry is telling me that he has given up his mainstream BBC1 meet-the- people show, Lenny Goes to Town. "Saturday night television is a strange arena," he says. "I enjoyed the affection from audiences, but there was a sense that the people in the studio were having a better time than the people watching at home. I'm not a game-show host. I don't want to have to say, 'Hey, let's look at the scores'."
Instead, Henry is concentrating more on straight acting, channelling his natural magnetism away from gag-a-minute showmanship into the intensity of the clown who longs to play Hamlet. Following on from his role as Dennis - travel agent by day, soul singer by night, in the recent BBC1 film The Man - he is now starring in Hope and Glory, a major - and serious - new BBC1 drama by Lucy Gannon, creator of such hit series as Soldier, Soldier, Peak Practice and Bramwell.
His part as Ian George, a hotshot head brought in to turn around a sink school, involves no mugging to camera with silly faces or voices. George is an utterly committed teacher, dedicated to inspiring pupils rather than making them roll in the aisles. In one scene George is sitting next to a lonely new boy in the school canteen. Handing him some chocolate, he reassures the lad in low-key tones: "You'll soon make friends, get to know the teachers, and there'll be someone here to help you". Playing down his natural flamboyance makes Henry all the more convincing in the role. Like his old friend Robbie Coltrane, he appears to have made an effortless transition from comedy to drama. Henry says, "It's like putting on a new pair of trousers."
For all that, he is well aware that some critics will tut-tut at what they see as "counter-jumping". "What do you do with people like that?" Henry asks, the exasperation clear in his voice. "I'm having a career - do you mind? I'm trying to learn - is that OK with you? Is that fair enough? When Robbie Coltrane did Cracker, people went, 'Wow'. It was unassailably wonderful. Before that people had thought of him as a comedy guy. If people think of you as a comedy guy, they don't think of you as anything else. You have to get the other stuff out of the way if you want any breadth. So let's not do another variety show. It's nice to branch out. Look at Tesco."
Of course it's easier said than done. The title of Lenny Henry's new live tour is simply "Large!". The exclamation mark is important; it sums up all those "e" words we have come to expect from one of the country's most popular comedians: exuberant, ebullient, extravagant, expansive. The public see Henry as a loud but lovable. They are drawn to the idea of seeing "one of us" up there in the limelight giving it his all. Henry bypassed the "alternative" generation with which he grew up. He was never one for "Thatcher Out" comedy; he even appeared on The Black and White Minstrel Show, for heaven's sake. His appeal has always rested on less fashionable but more durable qualities: energy, affability and the sort of charisma that means you're funny without opening your mouth. He has the "X Factor" which compels audiences to watch him whether he is strutting his stuff as the ludicrous "sex god" singer Theophilus P Wildebeeste or presenting a serious report on famine from Africa.
Henry is popular across age, sex and race barriers. Indeed, you could argue that his very popularity - not to mention his marriage to fellow- comedian Dawn French - made him an obvious target for those who live by bringing stars down to earth with a nasty bump.
Charlie Hanson is the producer of Henry's sitcom Chef! "Lenny's popularity stems from the same qualities he showed on Tiswas [the anarchic children's programme]. People know there are going to be moments of madness. He's a larger-than-life entertainer who has a way with an audience. Lenny has always had a side to him that appeals to kids and that families could therefore enjoy. Although from the alternative generation, he has always been a family entertainer in that he appeals to a wide age-range."
Henry's full-on showbiz persona has only been enhanced by his high-profile hosting of Comic Relief nights over the years. That forum gives full rein to his most over-the-top, sometimes self-indulgent clowning. But there is much more to him than that. Beyond the bloke-down-the-pub persona lies someone who is carefully deciding how to prolong his life in the business at a time when the appeal of being the all-singing, all-dancing entertainer has palled.
His colleagues certainly seem to think the change of tack has worked for Henry. Nick Brown, the producer of Hope and Glory, says that "the first time you see Lenny in this he's on stage, and people expect him to play to the crowd. He has that natural charisma, but he worked a lot at reining that in. I love the idea that people will tune into this expecting to see a certain thing from Lenny and will actually see something completely different."
Things have not always gone so swimmingly for Henry. He admits to experiencing frustration in the past. He jokes about prejudice - "I can't believe I wasn't cast as Mr Darcy, I didn't even get a phone call" - but clearly there used to be anger bubbling beneath the humorous facade. "I felt I had a lot to be angry about," he says. "What I was angry about was how difficult it was to get any programming with any level of multi-ethnic casting - either in front of or behind the camera. There were no black or Asian faces in the Bafta nominations. It's the water against stone effect - it'll happen eventually - but it would be great to see a more truthful reflection of society in my lifetime. Coronation Street has only just got an Asian shopkeeper. Have you ever been up north? Lancashire is nothing but Asian shops."
But doesn't his own great success disprove his argument? The fifth of seven children born to Jamaican immigrants in Dudley, he has not looked back since winning New Faces as a 16-year-old impressionist. He moved seamlessly from the ITV "zoo" children's programme Tiswas to the BBC1 sketch-show Three of a Kind (with Tracey Ullman and David Copperfield), before landing his own BBC1 series The Lenny Henry Show and the BBC1 sitcom Chef!.
Yet despite vehicles such as the BBC2 sketch-show The Real McCoy, which Henry helped to set up, he still believes other black performers are not given enough opportunities. "I'm a black guy, and I get to be on telly. But that's unusual, so you get noticed. Felix Dexter is funny, John Simmit is funny, Junior Simpson is funny - why haven't these guys got a TV series? Good people aren't getting a chance. Society as a whole is more tolerant, but some black people don't think that. I'm sorry, but they want more and bigger change now, please - and I can't help but agree with them. I don't walk around outside Television Centre with a placard, but the entertainment industry really needs to change. Don't hold your breath, though."
Henry has just turned 40. His mother died recently. He's acquired a more reflective attitude to life. "I don't rush headlong into things any more. You can't force things - otherwise it looks like you're trying too hard. I was a yes man for a long time. But if you spread yourself too thin, it does harm. I was busy, busy, busy. But now I make sure I'm not juggling 10 balls because even the best jugglers can't do that. It sounds pompous, but now I try to ensure there's a level of quality in the work. Admittedly that's very difficult for someone who wore a red leather bikini with feathers coming out of his arse on Comic Relief night."
No doubt particularly after last week's tabloid firestorm, Henry is anxious to keep his and Dawn French's seven-year-old daughter Billie out of the limelight. "It's not her fault we're on telly. She went through a strange period of thinking her mum was a vicar and her dad was a chef. But we try to behave like a normal family. It's important that one of us is always there for her."
Henry's plans for the future include a probable second series of Hope and Glory and another sitcom. He is, however, struggling to find the right script. "My wife said the other day that 98 per cent of sitcoms aren't any good. So you have to make sure you're in the two per cent."
He has other ideas, too. After Lenny's Big Amazon Adventure, where he journeyed into the deepest rainforest for the benefit of BBC1's viewers, he is now plotting something even bolder. "I might cross the Atlantic with Tony Bullimore [the yachtsman who famously survived for several days in the capsized hull of his boat]. It's good to do things you're scared of. When you hit 40, it's important to take things on. I'm not even very good on a ferry, so this should be interesting ..."
'Hope and Glory' starts on BBC1 in June. Henry's live tour continues until 6 June