Gangly-limbed, baby-faced, floppy-haired, fidgety: it wouldn't have been too much of a stretch for Chris Addison to have passed for one of the kids on the most recent series of the Bafta-winning teen drama Skins. Or at least one of their older siblings.

So it came as something of a shock to many of the E4 show's viewers when it was revealed that his character, a youthful, Machiavellian school official, was actually the father of one of the little tykes. "Judging by how young he looks, David Blood must've conceived Grace when he was practically a foetus," wrote one blogger. Not quite. For Addison has just turned 40. And he's feeling it.

"On the set, there are two green rooms," the Mancunian comedian and actor reveals of the sixth series, which will be broadcast next January. "I passed the one for the kids, which has a pool table, but I don't recall seeing any chairs in it: they don't really need them. And there's one for the adults, which has massive, comfy sofas. And I thought, that's basically it, isn't it? There's the divide. Looking at those two rooms, I just want to go and sit on the sofas."

No one could blame him if he needed a rest: it's been a busy year. The star of The Thick of It began 2011 by welcoming in the third generation of Skins teens, became a regular on Mock the Week and hosted his own panel show called Show and Tell. This week he has his first DVD out – a live performance recorded last year – and on Wednesday he begins his biggest tour to date.

It's not as though he's just been performing, either: Addison also spent his time mentoring his fledgling Skins cohorts: "The kids are often away from home for the first time and there's an element of looking after them. There's a lot of emotional work being done, so you need a very nurturing atmosphere to support them through it. When you talk to them one on one, they're smart, bright, interested, interesting, and they want to know what you know." Having said that, "when there's two or more of them gathered in one place at the same time, it's a screaming lunacy".

It is a mantle – that of the veteran instructor – that Addison is enjoying. Show and Tell, he adds, was essentially a way of bringing new comics to a bigger audience (including 2010 Edinburgh Best Newcomer Roisin Conaty and this year's Fringe hits Nick Helm and James Acaster). "And they wanted an old hand at the centre of it. That's how I discovered I'm an old hand. It was quite a revelation."

Not such a revelation is the esteem in which Addison is held within the entertainment industry. Skins co-creator Jamie Brittain offered him a role on his show when he spotted him at an awards ceremony. This was not only because of his 16 successful years as a stand-up (just months after he started out, Addison won the prestigious North-west Comedian of the Year competition and he has been nominated for Edinburgh's Perrier three times), but also because of his uncanny turn in his first acting role, as the junior government adviser Ollie Reeder in The Thick of It.

Amid the swearing and bombast in the political satire, Addison forged a rounded character in a quieter manner – as arrogant as he was inept, as morally bankrupt as he was ineffective. A fourth series is scheduled for next year, and with shenanigans such as the Liam Fox-Adam Werritty controversy, there's plenty to inspire the writers.

But given the high praise unceasingly doled out to the show, does Addison think The Thick of It has diluted our response to incidents such as Fox's antics? "No," he replies. "It's a sitcom. It's a little bit like asking whether your whole opinion of how things are between cats and mice has changed because you've seen Tom and Jerry. And I know everybody within the media world likes The Thick of It, but it's really a cult show, you know. It's not like everybody's seen it."

That's true, but its third series was drawing in audiences of more than a million, so if his response sounds humble – it is. Addison has a tendency to be self-deprecating. "I have the build of a runner," he revealed on his last tour, "and the muscle tone of a very soggy trifle. In an uncovered state, I look like a child who has done a collage with some Twiglets."

"My brain's OK, my body's a shambles," he added, which is a strange admission. Not the body part: that's there to set up a rant about gyms. But his mental capabilities? Addison first made a big splash on the stand-up circuit with some beautifully considered pieces about the periodic table, evolution and anthropology. Hardly the sign of a brain that's just OK.

He's reinforced that reputation of being the thinking man's comic on Mock the Week. He never appeared during the controversial Frankie Boyle's reign – when, Addison says, the show was "a bearpit". Now, it remains a feisty programme, but "it feels lighter, less aggressive, there's a lot more opportunity to build stuff together".

This idea of collaborative joke-making is one that appeals to him. "I like watching shows when somebody has half an idea and there's a back and forth, and there's something in the room that would not otherwise have happened. Stand-up is great. There's nothing better than the live experience if you've got a show you're happy with and there's a good audience. But it's also quite the solitary pursuit."

It is one he is about to follow again with his new tour, which could well feed a new-found anxiety. "It's only in the past 12 months that people have started recognising me in the street. It's made me oddly self-conscious, that feeling that you're being watched. I think – and I realise this is odd coming from someone in such a "Look at me!" job – that I'm not a big fan of being the centre of attention. Serves me right for making a career out of being a big, mouthy show-off."

Talking about what serves him right brings us to Addison appearing in adverts for Direct Line, in which he plays an insurance salesman, while Alexander Armstrong and Amelia Bullmore play customers who come across as mildly unhinged. Is that what the insurer is trying to tell us? That to buy from them, you'd have to be, shall we say, eccentric?

"Ha, no. I'm pretty sure that can't have been the intended message. I think the idea was just to get funny people doing funny ads." And are those funny people selling out, as Bill Hicks would have it? "I've never subscribed to that point of view," he counters. "When I was a kid and Fry and Laurie were doing the Alliance & Leicester ads and John Cleese was doing Compaq, for me, as a comedy fan, it was like a little bonus, and I loved it."

Addison will say little about the tour. "Really, it's not a show about anything in particular; I wanted to make it more personal." His 2010 tour was similarly personal and, arguably, middle class. At one point he turned to his audience and referred to them as "you lot with Ocado on speed-dial". Was he not worried that he was narrowing his potential audience with such definitions?

"Well, what would you do?" he hits back. "The key to comedy is to talk about what you know. When I first started out, I played up to the northern side of my accent and had a cigarette on stage in an attempt to diminish my middle-class status. But I quickly realised that that's what I have going for me, that's who I am. The idea that you can only register things that are like you: you know, I've been to Shakespeare and found that, as someone not living in the 16th century in Venice, I just didn't get on with The Merchant of Venice. That's quite mad."

Mad or not, it seems to have got his blood pumping. And if he's as feisty and animated as that on stage, his audiences should get a good show whether they think themselves middle class or not.

The story so far...

1971 Born 5 November, grows up in Worsley, Greater Manchester.

1995 Works during the day while performing at night in open spots. Wins the CityLife North-west Comedian of The Year contest.

1998 First solo show at the Edinburgh Fringe, receiving a nomination for the Best Newcomer at the Perrier Awards. Since then has performed 11 times at the festival and been nominated twice for the Perrier Award.

2003 Starts writing Funny Money, a fortnightly finance column for The Guardian.

2004 Co-writes and co-stars with John Oliver and Andy Zaltzman in Radio 4's political satire The Department.

2005 Takes on the role of Oliver Reeder in the BBC's satirical comedy The Thick of It.

2006 Publishes his first book: Cautionary Tales for Grown-Ups. Followed two years later by It Wasn't Me: Why Everybody is to Blame and You're Not.

2008 Plays Dr Alex Beenyman in the BBC mini-series Labs Rat.

2010 Hosts the BBC programme Have I Got News for You after having been a guest. Appears in the series Skins as David Blood, director of Roundview College and father of third-generation main character Grace Violet.

2011 Takes part in the Comedy Takeover on TV channel Dave, while performing in Uncaged Monkeys with pop scientist Brian Cox. Begins filming a new series entitled Show and Tell and releases a DVD of his live performance at London's Bloomsbury Theatre.