Robert Webb arrives at the pub not looking much like a man who's later having his photo taken for a national newspaper: there's a hole in the knee of his jeans and two more in the elbow of his cardigan. He suggests we sit outside so we can smoke, which endears him to me enormously. When I offer to go to the bar, he eschews mineral water, instead asking plaintively, "Can I have a proper drink?" and ordering a pint of lager, which endears him to me even more.

Webb is friendly and funny and extremely likeable, but he seems unnecessarily worried about how he's going to come across in print. He says he doesn't like the kind of interviews in which journalists probe comedians for the hidden darkness that drives their urge to make people laugh. Not that there seems much in the way of hidden darkness. While his long-term comedy partner David Mitchell cuts a vaguely eccentric figure – at least until his recent marriage to Victoria Coren – at 40, Webb seems the height of normality: happily married to fellow writer and comedian Abigail Burdess (they worked together a couple of years ago on the BBC2 Dickens parody The Bleak Old Shop Of Stuff), resident in a nice part of north London, two daughters aged two and four. At one point, he uses the phrase "tempered by", which is hardly the most pretentious in the English language, but it causes him to sink his head in his hands. "'Tempered by'," he sighs. "I'm going to come over as such a wanker."

Still, it all comes as something of a relief. I don't know why I thought Webb might be hard work, but I did. Perhaps it was down to his TV persona. On the one hand, a few years ago he made a fantastic documentary about his love of TS Eliot, for which he interviewed Andrew Motion and Clive James, read out a beautiful poem written by his wife, and came across as thoughtful, clever and charming. On the other, he presents and narrates an awful lot of clip shows – 10 Things I Hate About, Great Movie Mistakes, Pop's Greatest Dance Crazes – ostensibly as himself, but in fact as a character based vaguely on the one he's spent 10 years playing in Peep Show: sneering, superior, smug. Apparently, I'm not the only person to make this mistake. "I'm not going to do any more Movie Mistakes, because I think people have started to think that I am this … cunt," he frowns. "I do get quite well paid for two days in front of a camera and one day doing a voiceover, but I think that's enough now."

Or perhaps it was because his career looks, from the outside at least, to have been pretty gilded. At school, he studied to get into Cambridge with the intention of becoming a comedy writer-performer: "It looked to me aged about 15 or 16 that lots of the people I really loved watching on TV, like Fry and Laurie, had all gone to the same place, and what you did is you got some quite good A-levels, and then you go there, and then you try and meet someone funny, and then you do Edinburgh. Yeah, I had a plan. It was kind of sick like that."

The plan appears to have worked almost from the start, despite what must have been the shattering impact of his mother's death from breast cancer midway through his A-levels: he dropped out of school, returned the next year and got the grades. He wasn't intimidated by Footlights' illustrious history, regardless of the fact that he was the first person in his family to go to university – "We came from a village in Lincolnshire and, without wishing to use the phrase 'working class', read the Daily Mirror and watched Blind Date" – and had feared it would be full of "public schoolboys in white silk ties singing librettos about Proust". Instead, he met Mitchell and they ended up vice-president and president, respectively. Within a few years of leaving university, the pair had their own TV sketch series, That Mitchell And Webb Look, which eventually won a Bafta, and the lead roles in Jesse Armstrong and Sam Bain's Peep Show, which grew from an idea to create a kind of live-action Beavis and Butthead into the longest-running sitcom in Channel 4's history.

In the play Fat Pig at the Trafalgar Studio, London, 2008. Photograph: Alastair Muir/Rex Features

Indeed, the only notable disaster in his career to date seems to have been an ill-starred attempt to write a column for the Daily Telegraph, where he took terrible offence at negative comments from the barmier, climate-change-denying fringes of the paper's online readership, and ended up getting fired after a year. "I wasn't particularly busy at the time, so what I should have been doing in three hours, I was taking a day and a half to do, while getting drunk. I'd sit in the garden, drinking and talking to myself, then go back upstairs, write another sentence, go, 'Oh, this isn't right.' I'd make such a meal of it. If I'd been more professional, I'd have just done it and got on with my life. But because I'd turned it into this three-day psychodrama, and then the bastards hated it, that was quite hard to take." He laughs. "And now they're the official opposition in most councils, it seems."

His next role is in an upcoming episode of Agatha Christie's Marple called A Caribbean Mystery. Superior Sunday night fluff, it has a good script by Charlie Higson, a cast that includes Anthony Sher, and is Webb's first ever straight acting role. "I was wandering around privately thinking, 'So what is it actors do when they don't have to get a laugh at the end of the line?' And it turns out they just fiddle with their props a bit more."

I had assumed that straight parts were where his ambitions lay, partly because, the clip shows notwithstanding, so much of his work outside Mitchell and Webb involves acting – from a West End appearance in Neil LaBute's Fat Pig to umpteen sitcoms and comedy dramas: The Smoking Room, Fresh Meat, even Ben Elton's ghastly Blessed, which was put out of its misery after one series and seemed an odd choice for someone so meticulous about his own writing that he and Mitchell would come up with 500 sketches for each of their series, then abandon 400 of them. "Well," he says, "if the co-writer of The Young Ones and Blackadder says, 'Do you want to come and audition for this?', you say yes."

He certainly seems more interested in acting than in the world of the comedy panel show, which Mitchell seems to have colonised. "It's always a bit nerve-racking. I don't really relax and enjoy it the way David does. I don't mind coming second to David in a Who's Witty competition because, frankly, so does everyone else, so I don't turn up as often on those."

But he shakes his head vigorously when I suggest he has a desire to pursue serious acting. "No! I mean, I wouldn't mind it. I get asked every now and again, and it's nice to be on those lists, but I get slightly chippy about the idea that you're 'moving up' in some way. I'm not particularly itching to be 'taken seriously as an actor', because I've been taken very seriously for the stuff I've been doing up to now."

Nevertheless, he has been thinking about his future. "I'm feeling around for what happens in a post-Peep Show world. Technically, we've got a commission for series nine next year, but there's a vague feeling that it's winding down a bit." He recently had a conversation with one of the writers that led him to the conclusion they might not be making any more. "I wouldn't expect them to go through a billboard on the edge of a cliff in a double-decker bus and explode – we're never going to shoot it in the head quite like that – but it might be time to plan for what happens afterwards. I've been sort of coasting on Peep Show. So now it's kind of, 'When I grow up, I'm going to have to be an actor if I'm not careful.'"

In addition, while his partnership with Mitchell isn't over – they just completed a new series called Ambassadors, in which they play two British diplomats in eastern Europe, alongside Keeley Hawes, Matthew McFadden and Tom Hollander "as a sort of Prince Andrew-type trade envoy" – their collaborations are becoming more sporadic, which has had a positive effect on their friendship. "Now I hardly see him, it's the most cloudless relationship you've ever seen."

With David Mitchell in the 2007 film Magicians. Photograph: Sportsphoto Ltd/Allstar/Universal

When they met, Webb says, they'd been drawn together because they seemed quite similar. "He slightly reminded me of me, being an upstaging little shit. I mean, I was appalling at that point, because I'd gone to enormous trouble to get to university, my mother had died, I'd gone back to school for a year, and there was just a sense of 'I'm here now, and it turns out I do know what I'm doing', so by my second year at university I was really quite grand." But at the height of the sketch show's success, when they went on tour, they were barely speaking: "I was getting married that Christmas and David was the best man, and he had to stand up and say nice things about me. He says in his autobiography that he was really worried, because we really weren't getting on. It was getting a little bit pathetic. We'd just seen so much of each other. It's a lot for two people who are not in love and don't have sex. It's a sort of tetchy marriage."

It's easy to forget just how big That Mitchell And Webb Look was partly because, unlike a lot of their contemporaries, they didn't really go in for heavy marketing or spin-off merchandise, but their tour ended at Brixton Academy, as big a venue as you can play without getting into the realm of arenas. He doesn't give the impression of missing that kind of thing much. Instead, he finds himself "pottering about". He has an idea for a novel and a semi-autobiographical book about masculinity – "It's basically the only way I'm going to get to do an autobiography unless I get cancer or survive a high-speed car crash" – and a "half-idea" for a film, despite the fact that his experiences in the world of cinema thus far have been a little mixed. He's proud of the Mitchell and Webb film Magicians and last year's British romcom The Wedding Video, despite their meagre returns at the box office. "They spent a fortune putting adverts for it on ITV during the Olympics," he says of the latter, "when no one was watching ITV." By contrast, he so hates 2006's Confetti, an improvised comedy in which he and Olivia Colman played a naturist couple, that he once upbraided the film critic Mark Kermode for saying it was good: "He likes Confetti and he doesn't like Star Wars. I think that just relieves us from the burden of ever having to take Mark Kermode seriously again." Making it was "just an unhappy experience. Improvising, in May, while naked, standing around in a garden. So cold." His misery was compounded by the fact that, he says, the director assured him his genitals would be pixellated in the finished film, but then declined to do so. "I should cover myself, because she's a bit litigious, by saying that is not how she remembers it. But it is what I remember." He sighs. "I knew I was going to be naked, but I wasn't expecting eight- to nine-second shots where I'm just competing with my own cock for the attention of the audience. And losing."

You would think the experience of unexpectedly seeing your own penis on a movie screen might render you impervious to anything life might throw at you. But apparently not. Despite the ongoing success, Webb says he's still bothered what people think of him, which explains the business with the Telegraph commenters and his concern about how he appears in print. "People go, 'You shouldn't care', and you go, 'But I can't help how I feel.'" He drains his pint and corrects himself. "I shouldn't be grumbling because everything's going fine," he smiles. "I sort of think, doing the voiceovers for adverts and Movie Mistakes and things like that are on this side of the ledger and then, if you can do a documentary about TS Eliot and the odd play, then people won't think you're a complete twat. And it turns out I care whether or not they think I'm a complete twat."