The American magazine writer EB White once declared: “Humour can be dissected, as a frog can, but the thing dies in the process and the innards are discouraging to any but the pure scientific mind.”

Stewart Lee’s comic style is a gleeful two fingers up to this gloomily unambitious rule: he makes jokes and then self-consciously analyses them, and the analysis itself is a further joke that can be analysed, and so on for as long as he sees fit. The disassembled amphibian is really Schrödinger’s frog: both alive and dead simultaneously.

Even when, as here, Lee is pretend-self-hatingly monetising a collection of detritus, he goes the extra mile. Where other comedians might slap together a sheaf of newspaper columns with a desultory introduction, Lee festoons them with lengthy footnotes in a different voice. As he explains, the columnist persona “Stewart Lee” is a different character from the standup persona “Stewart Lee”, and both are different from the compiler of this collection. “The only voice you can trust in this entire book is the one the footnotes are written in,” Lee writes in the introduction, and since this text is not in a footnote, it’s obviously a lie as well.

The book is all about lies, of course, since it gathers Lee’s Observer columns about Brexit between 2016 and 2019, written in the character of a man not quite in command of his “over-finessed language” but with a deeply felt tone of abusive despair. Mercilessly he reproduces the most insulting comments left below his pieces online, like little turds proudly deposited by uncomprehending dogs, who are now deservingly shamed anew to a wider audience, for ever.

On many pages the footnotes, which recount tastily bleak showbiz anecdotes or run off on whimsically discursive tangents, take up more space than the main text, so it’s a bit like reading a critical edition of Milton, only funnier. While also (like Brexit) more depressing, particularly in the haunting scene where footnoter “Stewart Lee” recounts meeting Michael Gove – with whom he once worked on a 1990s comedy TV show – in a motorway service station in the autumn of 2018.

“What are you going to do about the mess you have got everyone into?” the comedian asks. “‘I don’t know,’ said Gove, looking genuinely bewildered.” Right. Thanks.

Certain running themes emerge. The footnoter “Stewart Lee” enjoys getting the names of things deliberately wrong, as when he repeatedly refers to the Scottish singer Pat Kane’s old band as “The Kane Gang”, and he often complains – rather like the politicians he despises – that his critics have taken him out of context. Every so often, the columnist “Stewart Lee” squeezes another middle name into the moniker by which he refers to our current prime minister, until it has become “Boris Piccaninny Watermelon Letterbox Cake Disaster Johnson”. There is in the columns a broad streak of toilet humour, which signals when the columnist “Stewart Lee” is too wearied to keep up the pretence of poshness, but which also accurately mimics the way pro-Brexit arguments have been conducted by men and women pistoning their rancid gums with no regard to how things actually are in the world. Thus: “This apparently showed that there was no need for a British border in Ireland, because of blah blah blah shit piss wank.”

This is all very entertaining, but the device whereby one persona footnotes another really blossoms with a full commented transcript of Lee’s standup show, Content Provider, as performed in April 2018 in front of BBC cameras in Southend, a town he eulogises at one point as “this hive of racists”. I should at this point say that for literally decades, my friends have been telling me that I should check out Lee’s work because I would really like it, which is precisely why I have always avoided it until now. It is therefore really irritating to find that I like it quite as much as they said I would.

But it’s the commentary that really, as they say, “adds value”. The footnote-composing “Stewart Lee” discusses issues of timing, vocal timbre, and music-hall history with nerdy delight and flashes of knowing pomposity. The footnoter “Stewart Lee” also expresses regret for some of the standup “Stewart Lee’s” improvising decisions, straight-facedly overexplains jokes, and goes on withering rants about rival comedians. It’s just a shame there is no two-page exposition of the sonorous phrase “Taiwanese fist glove”.

The overall effect of this metatextual performance is rather like a reversal of Nabokov’s Pale Fire: as if the sober artisan poet John Shade were offering commentary on the insane fantasies of Charles Kinbote. And just as neither of those characters is Nabokov himself, so neither of these Lees is Stewart Lee: his relentless, onion-layered self-irony is actually a brilliant vanishing act.

• March of the Lemmings is published by Faber (RRP £14.99). To buy a copy go to guardianbookshop.com. Free UK p&p over £15.