When legendary Radio 1 DJ John Peel died suddenly in 2004, it left a musical and cultural void that has never quite been filled.

As several generations of indie-kids weaned on ground-breaking sonic obscurities ranging from DIY post-punk to dub reggae, techno and experimental noise went into mourning, it became increasingly apparent just how much Peel changed the landscape of popular culture forever.

One of those who knew this already was writer and some-time performance poet John Osborne, whose very personal one-man homage, John Peel's Shed, was one of the most heartfelt hits of last year's Edinburgh Festival Fringe. Inspired in part by Osborne's book, Radio Head: Up and Down the Dial of British Radio, which charted his experience listening to a different radio station every day, John Peel's Shed was an appropriately lo-fi geek's-eye view of a record-buying subculture which has since gone viral.

It's only fitting, then, that Osborne's current tour of John Peel's Shed arrives in Scotland for a quartet of one-night stands mere weeks after the launch of The John Peel Archive. This major interactive website will in time enable browsers to rifle through Peel's record collection one letter at a time, opening up future generations to a pandora's box of eclectica beyond the X Factor mainstream. Such an archive is vital on an emotional level as much as a historical one, as Osborne explains.

"People remember John Peel with such affection," he says, "and something like this is kind of intriguing and fascinating for John Peel fans. But I suppose there's been lots of things that have happened since his death, like the John Peel Centre for the Arts in Lowestoft and things like that. John Peel really has tapped into something. His death seemed to affect everyone. I don't think there's a death that's affected so many people. People can really pinpoint where they were when they heard what happened, and I think a lot of people realised just how important he was, whereas before I think we probably took him for granted. But this site goes some way to making amends for that, and I think it's in the right hands."

If Osborne hadn't won a box of Peel's own records in a competition back in 2002, it's unlikely that his ongoing adventure in radio would have borne such fruit. This is the nub of a show that sees an initially nervy-looking Osborne appear to grow in stature as he goes deeper and deeper into his sonic adventure, spinning tunes and providing facts and figures as he goes. This has been the case too, it seems, for the production itself as it has developed.

"After the book came out, the first incarnation of the show was on my local community radio station," Osborne says, "and that all came together really naturally after I'd started thinking how I'd do something similar to the book differently if I did it live. The best album ideas all come together really quickly, and it was the same with this, but I never expected it to become as big as it has done. I've done poetry gigs for the past five years, so Edinburgh wasn't unknown to me, but I'm not an actor or a natural performer, and I'd never written a full length show. It's also really personal, about my relationship with John Peel and this box of records, so I needed someone to look at it objectively in a way that I couldn't, because I didn't really know what I was doing."

Osborne emailed his early scripts to Joe Dunthorne, author of the novel, Submarine, and a friend from Homework, a spoken-word night at Bethnal Green Workingmen's Club, where both are resident performers.

Together the pair gave John Peel's Shed dramatic shape.

"There's a record played in it every 10 minutes," Osborne points out, "so it feels like you're writing five 10-minute pieces. In a way it's a double-act, with me and this record player doing the show together.

So overall it's become a lot better, because I'm more confident now as a performer. The passionate bits are more passionate, and the funny bits are funnier. It's different to when I did it in Edinburgh. I'm more comfortable and relaxed onstage now, so in a way the hard bit's over."

Like Dunthorne and the other Homework residents, Osborne is one of an increasing number of performers whose work comes from a hybrid of live art, spoken-word and what in punk days of yore was called alternative cabaret rather than a formal theatrical root. Just the sort of thing, then, that might have ended up on Peel's programme alongside the likes of John Cooper-Clarke, Ted Chippington and American monologist Eric Bogosian.

Osborne cites the likes of Edinburgh Comedy Award Winner Tim Key, Ross Sutherland of live poetry collective Aisle16, and ubiquitous left-field stand-up Josie Long as his peers and fellow travellers. All three, like Osborne, sit between several stools, genre-wise, and you get the impression from him that this is a quirky but comfortable place to be.

"I just like things that you can't really explain what they are or categorise them in any way," he says. "They just do their own thing."

Even as Osborne gears up for this year's Edinburgh Festival Fringe dates, as with many bands played by Peel, Osborne is gearing up for his equivalent of the difficult second album.

"It's slightly scary," Osborne admits, "but there are some difficult second albums that work. I'm writing another book and another show at the moment, and I just want to try and make enough time and have enough energy to do something really good. I've got a lot of good people around me who I can try things out with and talk to about stuff, so I'm really lucky in that respect, but I don't want to rush into things either."

Regarding John Peel's Shed, Osborne explains: "I think it's something I'll always perform, but this year's Edinburgh dates are definitely going to be the last for some time. I imagine I'll do it for special occasions, and I know I really owe a lot to John Peel's Shed, but for the time being I think it's right to put it to bed for a while and move on to something else."

As for the great man himself, his legacy is everywhere to see and hear.

This isn't just in the ongoing archive and numerous websites documenting the sessions and other arcana that made Peel's programme so unique. It's apparent in a culture that in some ways seems more prepared to look beyond the mainstream, even as sounds Peel revealed to the world three decades ago trickle down to inspire younger generations of sonic explorers.

"The gap left by John Peel has not been filled by an individual presenter," Osborne points out, "but by an entire station. That's what 6Music is about and that's what it's for. It doesn't matter whether it's Lauren Laverne or Marc Riley or Gideon Coe presenting. You can hear the spirit of John Peel in every show."

John Peel's Shed, Lemon Tree, Aberdeen May 22; Perth Theatre, May 23; Paisley Arts Centre, May 25; Tron Theatre, Glasgow, May 26; Underbelly, Edinburgh Festival Fringe, August 7 to 12.

www.johnpeelsshed.com