You probably wouldn’t guess it from his mastery of the material and the fluency and control of his delivery, but Stewart Lee is also road-testing a new show for Edinburgh.

In 2004, after a few years away, he turned up to the festival with ‘Stand-Up Comedian’ – and, as the choice of title might suggest, it was a bold declaration that the comedian-cum-novelist-cum-critic had returned to his true vocation. Zeroing in on Americans, Ben Elton and Gary Lineker’s “velvet owl face” and wrapping up with an extended version of the much-loved routine about the tributes to Princess Diana left outside Kensington Palace, the show (available here) is one of the funniest things I’ve ever seen.

The following year Lee was back in the Scottish capital with the self-deprecatingly named ’90s Comedian’ (DVD here, courtesy of the lovely people at Go Faster Stripe), part personal mission to make jokes that Joe Pasquale couldn’t steal and part cathartic crusade to respond to his experiences in the wake of the controversy surrounding ‘Jerry Springer: The Opera’. With that out of his system, and fatherhood having crept up on him in the last few months, would we see a more mellow figure before us?

In short, no.

This new show was originally called ‘March Of The Mallards’, as Lee explains, in direct response to the American Right who appropriated ‘March Of The Penguins’ for their own ends, claiming that the penguins’ monogamous relationships and close-knit family units are nature showing us how to live morally. Mallards, you see, reproduce by gang rape and have also been known to indulge in (he relishes the phrase) “homosexual necrophilia”…

Realising he didn’t have enough mallard-related material to spin out over a full hour, though, Lee plumped instead for a more familiar-sounding title, ’41st Best Stand-Up Ever!’. Taken from his position on recent Channel 4 list programme ‘100 Greatest Stand-Ups’, stalled just outside the Top 40, “it’s both humble and arrogant” and allows him free rein to ruminate on his favourite subject, comedy itself – and indeed the show kicks off with a long segment on Tom O’Connor. If you think all that sounds a bit tediously and self-regarding, then you’d be very wrong – Lee is very often at his funniest when trying to pinpoint with that characteristically relentless attention to detail exactly what it is that makes something funny.

Lee is as prepared to mock himself, detailing the embarrassment of going to WeightWatchers, as he is others (Russell Brand, Stuart Maconie, his mother). Most of his vitriol is saved up for “the 20 or 30 people who run TV” and Sun columnist Richard Littlejohn. The latter is attacked as part of a segment about the Suffolk serial killings and that most unsacred of cows, political correctness, which, for its sheer genius, is most probably the bit destined to live longest in the memory. It isn’t spoiling the show in any way to mention that other subjects include the potato peach aphid and the possibility that Carphone Warehouse and online lingerie site BeCheeky.com might be “the fronts for racialist organisations”.

And, as befits a comedy theorist, it’s not just about the material itself; it’s also about the way it’s packaged, about the deliberate pace and structure (there’s a big difference between deliberate and laboured, whichever Independent critic labelled him the latter), about the language in which it’s framed and about the intellect that stands behind it all. No wonder Time Out suggested it’s worthy of winning the Booker Prize.

No pen and paper for Lee – either the show’s very nearly complete and he’s only reminding himself how to stay on stage (it’s tiny, and he accidentally steps off mid-flow on at least two occasions) or he’s sufficiently confident in himself and his material not to crave or even need the audience’s explicit approval.

Obviously, that could be a bad thing in someone who is ultimately paid to entertain people, but with Stewart Lee you know you can feel confident that wherever he takes you it’ll be inspired. Hence the show’s conclusion: a man, stood on stage with a soft toy balanced on his head, in complete silence.