Loitering outside the BBC’s Western House, home to 6 Music and Radio 2, on a sunny Saturday, is a band of straggly autograph hunters. Who might they be waiting for? Could it be BBC 6 Music’s Adam and Joe, recent winners of Best Radio Programme at this year’s Broadcasting Press Guild awards and currently at No 1 in the iTunes comedy chart?

“No. You can see them look at us and go: ‘Nah’,” says Joe Cornish. “It’s good for our egos to get ignored . . . every week.”

Adam Buxton, the short, smiley one, is mid-broadcast, padding about in his socks. Cornish, the “man giraffe” and slightly forbidding one, is sunk in a sofa, recovering from a nasty bout of shingles. “We don’t have enough weird fans. I want more. In fact, there’s no such thing as a ‘weirdo’ fan for me.”

“No, they’re just eBay freaks,” says Buxton. “I like that we’re not famous enough to get that kind of attention. There’s always been a small hardcore who get what we do. Then a large group of slightly mystified people who don’t get it.”

“And a much larger group,” adds Cornish, “who don’t even know we exist, consisting of about 50 million.”

Despite their honesty about the relative nature of their celebrity, the pair’s status as the nation’s “fantasy best friend” was cemented with their Channel 4 show The Adam and Joe Show, back in 1996. At a time when new laddism was inescapable, they spoofed Hollywood films using soft toys and got Adam’s Dad, a former Daily Telegraph journalist, on board, taking him clubbing in Ibiza and to rock festivals. “We tried to get as far as away from Loaded as possible,” explains Buxton. “No football, tits or boozing. It was all nerdy things.”

Since the show ended in 2001, they have had stints in America and Japan, been stars on XFM and-attempted solo careers, but it has been their new BBC show that has once again won them acclaim. “As much as we try to have solo success,” notes Cornish, “the thing we seem to get rewarded for is just when we’re being lazy and talking rubbish to each other.”

At this point their producer announces that they have got ten seconds before they are on air again and asks: “What’ve you got?”

“I’ve got shingles,” mutters Cornish. With that they both put their head-phones on and banter for ten minutes, amusing each other with the fact that they have never seen each other naked, arguing over whether they have “trangressed the unwritten booby rule” by mentioning breasts before midday, and surmising how they too could get punched by Amy Winehouse (“Move her crack pipe,” suggests Cornish. “But then she’ll just eat it in a sandwich,” adds Buxton).

“We’ve known each other so long we are quite good at talking rubbish to each other,” admits Cornish afterwards. “But the worst aspect of radio is that you have to fill dead air. So you often say something you regret.”

This is of course something that makes them addictive listening. There isn’t much they won’t say. It has led to some painful on-air exchanges. Particularly over a segment of their show called Song Wars. It’s the reason we are meeting, as the pair have just released a compilation of the songs they record at home and then “battle” each week on the show. Inspired by a shared theme, unexpected gems have been provoked by subjects such as height and Ikea meat-balls. The winner is voted for each week by the listeners.

“Originally I thought it sounded like much too much work, and then proceeded to win week after week,” smiles Cornish.

“I was genuinely upset,” sighs Buxton. “When Joe would get a landslide victory it hurt. He got 95 per cent one week. My song wasn’t that bad.”

“It was bad.” Having weathered the Song Wars storm (they are now drawn even), what next? A move to Radio 2?

“Yes,” says Cornish, for once serious.

“We don’t, like [Russell] Brand, have big, hair, a ‘drug hell’ past or enjoy being in the tabloids. But we’re prepared to do whetever it takes.”

Finally, it seems the assault on “the Big British Castle” has begun in earnest. Sort of.

Adam & Joe’s Song Wars: Volume One (BBC Music) is out on iTunes

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