If Adam Buxton’s hilarious Festival Song isn’t this summer’s biggest hit, then there is no God. His razor-sharp dissection of the green-welly festival is so excruciatingly spot-on, it’s a wonder Cornbury, the Big Chill and the rest haven’t cancelled out of sheer embarrassment.

“Load up the 4x4, it’s festival time. We’re stuffing the chill bag with nibbles and wine,” sings Adam’s fruity-voiced narrator, as he recalls how awful festivals used to be when there was “nowhere to charge your mobile phone and nowhere nice for doing poops”. And how great they are, now they’re in stately homes with “ace” global cuisine and “a really nice crèche” where you can leave your kids “while you get off your face”.

Yet try prostrating yourself before Adam’s mighty genius — or that of his equally talented BBC6 Music co-presenter, Joe Cornish — and neither of them will hear a word of it. “If you knew how easy it was to do, you wouldn’t be so impressed,” insists Adam, as we sit outside a south London pub. To prove it, he knocks out a catchy new banjo-driven original just for me, using GarageBand on his Apple laptop.

Besides their quietly successful side projects — the garrulous, bearded, shorter, sillier Adam (left in the picture) directs quirky pop videos for Radiohead; the taller, quieter, drier Joe is working with Edgar Wright on a Marvel comic film script called Ant-Man — the cult Saturday-morning show they present on BBC6 Music has just been named Radio Programme of the Year at the Broadcasting Press Guild awards. “Apparently, it’s quite important,” says Joe, 39. “It’s very flattering,” agrees Adam, also 39, “because our usual feeling is that we’re off the critics’ radar.” He is delighted that, in the very same week, Uncut magazine put them in the same comedy league as Chris Morris and Bill Bailey.

Not that fame is something they are actively seeking. “We’ve watched loads of our contemporaries rocket off, like Matt Lucas and Dave Walliams,” says Joe. “Dave once said to me, ‘What’s it like to be famous?’ And now he gets burgled whenever he leaves the house, because he’s so famous, everyone knows where he is. I don’t envy that at all.” Also, if they ever became household names, their act might go through “the shit mirror”.

Listening to the show is like sitting in on a pub conversation between two extremely witty, frivolous, pop-culture-literate mates. Besides Song Wars — their weekly competition to see who can record the best song on a given theme (for example, instructions for cooking meatballs) — they digress on anything from celebrities they’ve met (Joe wonders whether it was really a good idea to approach the actor Christian Bale and show him a homoerotic cartoon version of himself in a comic) to what name they’d call their team if they were on The Apprentice. “I’d call mine the Ambitialiser, because it combines visualisation with ambition,” declares Adam. “I’d call mine the Winnerz. With a ‘z’,” says Joe.

They have been keeping up their studied, ironic patter since they met at Westminster School in the 1980s, united by a love of bratpack movies, Not the Nine O’Clock News and anything that had TM after it. “We were very full of ourselves — as you are when you attend a fee-paying school in the middle of London that requires you to swan round dressed like the Blues Brothers,” says Adam.

After stints at art college (Adam) and film school (Joe), they answered an ad in NME inviting members of the public to submit video sketches for a comedy talent show called Takeover TV. It led, in 1996, to four series of The Adam and Joe Show on Channel 4: a mix of amateur stunt movies (Adam going to an unwitting Essex brewery to see how easy it is to stage a piss-up in a brewery) and spoofs of Hollywood blockbusters (Toytanic, Toytrainspotting and American Beautoy, acted out by soft toys).

The odd thing is that for all their success as presenters, it was the very last thing they ever wanted. “We didn’t even want to call it The Adam and Joe Show,” says Adam. “And we only filmed ourselves doing the links because the producer insisted.” Canny producer. He has created the wittiest, most promising radio double act since Ricky Gervais and Stephen Merchant languished in obscurity at Xfm.

6 MUSIC: THE SECRET’S OUT

6 Music feels like one of those secret cults that, all of a sudden, everyone you know is listening to. It was launched in 2002, but I first heard about it a couple of years ago when a friend said she couldn’t believe she’d found a radio station that played old Smiths, Echo and the Bunnymen and Kate Bush along with cool new stuff. It is like my record collection, but better, hitting the nail on the head for thirtysomethings who grew up taping Janice Long and John Peel in the 1980s and love quirky pop from Bowie to Björk. “Appealing to music lovers is the most important factor,” says Lesley Douglas, the controller, “but generally, the target age is somewhere between Radio 1 and Radio 2 — 25- to 44-year-olds.”

If you feel alienated by Radio 1’s occasionally cheesy laddishness (Chris Moyles), limp R&B and faux indie, but too young for Wogan, this is the station for you. You will like the marked lack of banter — the ones that do it, like Adam and Joe, and Stephen Merchant, are cult comedy. My favourite 6 Music DJs are Queens of Noize, Liz Kershaw and Gideon Coe. Steve Lamacq’s emphasis on breaking new music such as Arcade Fire is also laudable, and Craig Charles’s Saturday funk and soul show is unmissable. 6 Music gave Kate Nash and the Ting Tings their first sessions, and Santogold is currently on heavy rotation. “6 plays music you would not hear on mainstream radio elsewhere,” says Douglas. All hail to that.

Bethan Cole

Editor's choice

• The 100 Best Films of the Decade
• 70 facts you didn't know about Marvel
• The 50 Biggest Movies Of 2010