Stewart Lee, widely regarded as one of the UK’s most influential live performers by comedians from big names such as Ricky Gervais to newcomers such as Josie Long, ended his stand-up career in 2000 shortly after a gig in Fulham where a bloke kept shouting: “Tell more jokes! We’ve paid to hear jokes!”

“I thought, it’s not even fair that I’m here,” he recalls. “They’ve got every right — I’m not what they want.” Flick forward seven years and during the Edinburgh Festival that same comedian is holding an audience of more than 400 spellbound with a routine that, on paper, should fail every single time.

The show is called 41st Best Stand-Up Ever, and he’s riffing on a Channel 4 poll that voted him into that hallowed spot, above the late, much-missed Irish comedian Dave Allen, Steve Martin and Tommy Cooper. One of Lee’s points is that these polls cannot be trusted — not least because everybody’s all-time comedy favourites usually involve the scene from Only Fools and Horses where Del Boy leans against the bar in the boozer and falls through an open serving hatch.

Lee describes the scene repeatedly, setting its banality against his mother’s indifference to her son’s comic talents and his failure to secure a television series, which was initially offered without even the need for a pilot. “This is what you find funny,” he repeats, sinking slowly to his knees — “Del Boy fell through the counter. You like that. Del Boy fell through the counter” — until finally he’s curled up on the floor, repeating it again and again and again. It’s mesmerising, intense, hilarious, upsetting. And there’s something about him — the performance, the timing — that’s making every one of those 400 people laugh just as hard as they can. So what happened between 2000, when he was practically booed off the stage and gave up performing, and 2007’s show, where they craned to hear his tiniest whisper?

He smiles. “When I came back to stand-up for the first time in 2004, I was literally performing some of the same routines I’d been doing at the end of the 1990s,” he explains, as we work slowly through sandwiches in a hotel bar near Broadcasting House. “As recently as 1997, I’d been doing a month-long show to 20 people a night. In 2004, I was sold out for the entire run, and it was really odd to be reviewed positively for the things I’d been damned for. I went from being boring to hypnotic, from patronising to intelligent. And it can’t have changed that much. Maybe it looks different coming out of a fatter, older man. I looked more entitled to feel like that, whereas someone in their twenties — you assume it’s an affectation.

“But the biggest difference was that when I was doing stand-up in 2004, Ricky Gervais said in an interview that I was the best stand-up ever — and I put that on the poster.”

It’s strange to find Lee so self-deprecating in conversation. His comedy — from 1990s television success with Richard Herring in Fist of Fun, through controversy over Jerry Springer — The Opera, which he co-wrote and directed, to today’s iconic stand-up status — has always seemed confident and certain, picking off targets with a limitless vocabulary and expert timing. He happily faced down the rage of the religious right over Springer with arguments drawn from William Blake and would publicly bemoan the attitude of the BBC2 controller who took him and Herring off the air.

Perhaps it’s as he says: he suits his age. At 40, he’s married with a child and clearly finds contentment in his family life. Then again, it could be down to the momentum of his recent success. Having lost the television series, he suddenly found it offered again — and the BBC was effectively prepared to let him do exactly as he pleased on air. The result is Stewart Lee’s Comedy Vehicle, six 20-minute stand-up sets where he destroys the banality of today’s flimsy culture, from celebrity hardback books to, well, lists of 100 Greatest Stand-Ups. And he pulls off the Del Boy routine, right down to lying on the floor completely off camera, in a move that shouldn’t, but somehow does, work on television.

“There hasn’t been anything like this in stand-up on television for about 40 years,” he says. “Not since they put Dave Allen in a chair and focused slowly in on him with a single camera. His stand-up was the kind they say never works on television — it was slow, with lots of pauses in it, and there were stories that took seven minutes to get to one punch line, with no obvious laughs along the way.

“What’s good about this show is that they let things run long — they let routines like the Del Boy one unfold. I’m very lucky because, as a script, there’s no way it would get commissioned. It’s only the weight of good press that’s got me here. I mean, I’ve had reviews saying I’m the best living stand-up. I’m not saying that’s the case, obviously, but that’s what helped get this made. It’s not the kind of stand-up that would also make a funny magazine article.”

This sort of material, he explains, required an unusual comedy education. Lee grew up in the West Midlands and starting going to music gigs in the early 1980s (he reviews for Culture’s music pages), when so-called alternative comedy was at its creative peak. His first experience of comedy was the Comic Strip’s Peter Richardson opening for Dexys Midnight Runners. After that it was Phill Jupitus doing poetry, supporting Billy Bragg, and Ted Chippington, who performed in an odd, papier-mâché head, introducing the Fall.

“I was lucky — or unlucky, from a commercial point of view — that, as an impressionable teenager, they were the first people I saw,” he explains. “Most of them were people for whom comedy is an art form in quite a distinct way. If the first gig I’d ever gone to was a night at the Comedy Store, it would have been different — but I thought that was the way comedy was supposed to be.”

With the rise of Newman and Baddiel, laddish comedy and the chain-store nature of clubs such as Jongleurs, he felt beached and alone. Now, though, there are comics such as Daniel Kitson, Josie Long, Robin Ince and Danielle Ward who believe as much in the art of stand-up as he does, organising gigs in museums and hailing Lee as an uncomfortable sensei.

“Alternative comedy like The Young Ones was for all the weirdos to like,” he says. “And then it became something that advertisers would use or it would get its own stage at a sponsored festival. I think this new wave of comics is trying to reclaim parts of comedy for the weirdos, to marginalise parts of it again with stuff you won’t get in a mainstream comedy club. It’s great for me because I feel most TV comedy has nothing to do with me. I’m baffled by most of it. In the mid-1990s, I did at least feel part of a school of thought. That’s why I’m so excited they’ve all come along now.” He grins. “I’ve been doing stand-up 21 years now, and I’ve come into fashion three times — this is the third time. If it happens twice more before I’m 60, I’ll have enough money to retire.”

Stewart Lee’s Comedy Vehicle, BBC2, 10pm, from tomorrow

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