Four years ago Stewart Lee was mugged by a gang of teenage boys. He was in north London, walking home from the shops, and they surrounded him, threw fireworks at him and just when he thought he had scared them away, one of them came from behind and punched him in the head. “And almost, when I was being punched in the back of the head, I was thinking, ‘There might be a show in this,’” says Lee. That’s insanity, I say. “That’s the luck of being a stand-up. If a bad thing happens to you, it’s a short journey to it becoming a routine.”

In the case of Lee, the journey is never that short. The comedian, named the “greatest living stand-up” in a list published by The Times in 2018, has been wondering how to make a routine out of that “humiliating” incident for four years and counting — and it’s still not quite there, he says. “I know there’s probably the spine of an hour in that, but it’s not ready. It’s percolating. It probably needs some other incident to crossbreed with it.”

Lee is not a comedian who dashes things off or leaves things to chance. He likes to refer to himself — only semi-ironically — as “Britain’s master of the multi-callback ending” for his ability to weave stand-up hours that loop round and back in on themselves like an Escher painting, glorying in repetition, seeded punchlines, and seeming blind alleys that open out into triumphant waves of laughter. He leads his fans on a merry dance and they love to follow him. So much so that when he was performing his live show Tornado in Bexhill in March and a giant prop shark malfunctioned, falling from the ceiling too early and nearly killing him, the crowd thought it was all part of the plan. “I said, ‘Ah, that’s not supposed to happen,’ and everyone was going ‘ha ha ha’,” he says, miffed. It meant he couldn’t do his big ending. “But you can make something of that. A man saying, ‘I’m sorry I’ve not been able to do the important bit’ — the tragedy of that is funny. Isn’t it?”

Tornado comes to BBC2 this month as half of a double bill of filmed live shows. The other half is Snowflake, in which Lee tackles cancel culture and the “woke brigade” in typically astringent style, culminating in a routine that eviscerates Ricky Gervais’s supposedly “cancelled” controversial Netflix stand-up special, in which he “says the unsayable”. “Except he doesn’t. He says the sayable. As we all do. By definition,” Lee says witheringly.

When I see Lee perform Snowflake in Edinburgh on a sunny Saturday afternoon during the Fringe, that routine has added edge: a week earlier, Jerry Sadowitz’s show at the festival was actually cancelled when audience members and staff at the venue complained. Lee didn’t see it, but before the festival began he did recommend Sadowitz’s show on his website, with the caveat that his act “made conceptual sense when we all lived in a supposed liberal consensus”.

“The problem now is that there are comedians on our circuit that are specifically and explicitly from the right,” he adds. “So I think people can be forgiven for feeling differently about Jerry . . . The ground has shifted around him. Last time I saw him ten years ago, [his act] was still really good. But it’s a different world, unfortunately.”

We meet on a Monday as the Thistle Street Bar in Edinburgh’s New Town opens. Lee has just performed a morning work-in-progress show, titled Basic Lee, at the Stand comedy club. As usual, there’s not much “in progress” about it, the jokes about JK Rowling, jazz and the process of writing already finely tuned. Lee is in ebullient mood, although limping a bit (he did his knee in ten years ago doing a joke about Jeremy Clarkson “kicking a tramp to death” and it’s never been the same since, he tells me).

He is delighted by how the Rowling joke went down (“I can tell you now, without sounding arrogant, that is going to be a really, really good bit”) and an early-morning crowd who were very much on side. “They’re the Millwall fans of comedy,” he says proudly. “They’re loyal and tribal and they don’t like other comics. They say, ‘If you like me, you get bored of the other things.’ They’re thought of as snobs — but they push me on to do better things.”

He was less happy with the crowd for Snowflake on Saturday afternoon, when he didn’t perform the last part of his routine because the set-up didn’t go as well as he hoped. “There’s only really one thing that I can do,” Lee says. “And it’s a kind of duet with the audience, where you work off their responses, change it a lot some days, not so much other days.” He subscribes to the jazz pianist Thelonious Monk’s adage that what happens in the room is the show. “If the audience chooses to not understand something, you can have a go at them but in the end you have to let it go. Explain to them that they failed and now it’s not going to be what it was supposed to be. And that’s why it’s live.”

We decamp to the pub garden to escape some noisy drilling inside. About a decade ago, Lee realised that he was going deaf and he now wears a hearing aid, but still struggles with background noise. He thought he may have damaged his hearing from going to gigs and performing, but discovered belatedly that his deafness is hereditary. He spent the first year or so of his life in care before he was adopted and grew up in Solihull. He met his biological father for the first time in 2010 — “in a pub car park in Essex. The first thing I ever said to him was, ‘Hello, oh you’ve got hearing aids.’ And the first thing he ever said to me was, ‘Yes, all the men in your family go deaf and so will you.’ I thought, right, and I went and got tested. It’s made my act much better.”

For a few years before that he had been playing the same rooms he had for years and was wondering why his material was getting fewer laughs. He didn’t realise that he just couldn’t hear them. His shtick of coming down hard on audiences — “driving them forward to make them understand” — grew out of his deafness and by the time he realised, his onstage persona — frustrated, misanthropic, annoyed — had stuck.

The Stewart Lee who performs on stage is a character, though like all the best comedy characters, he is an exaggeration of all the things that are most irritating about him in real life. Such as? “He’s patronising, he doesn’t listen to other people, he’s repetitive, he doesn’t understand really obvious things, and although he’s broadly in the right position morally, he also gets pleasure from the vanity of thinking that he’s right.”

The real Stewart Lee lives in north London and is married to Bridget Christie, the award-winning comedian with whom he has two children, Daisy, 11, and Luke, 15. Is it a funny household? “No,” Lee says. “No, it’s not. Particularly not under lockdown. Comedians that live together don’t . . . perform.”

They do discuss comedy, although Lee says that Christie doesn’t like him watching her shows, so the last time he saw her perform live was in 2016. “It’s difficult with a male-female partnership; the assumption will always be — from the position of hostile parties — that the man is driving it along . . . That the man has done the best bits.”

They avoid talking about each other in their acts — partly, says Lee, because he couldn’t think of anything worse and partly because it distracts from the joke if people are imagining “Stewart Lee” whenever Christie says “my husband”. The boundaries are blurring a bit though, because Christie has written a new sitcom, The Change, for Channel 4, in which she plays a menopausal, married mother-of-two who leaves her useless husband (played by Omid Djalili) and disappears into the woods on a motorbike. “I said to her, ‘You know, when this comes out, everyone’s going to say that’s me.’ She said, ‘They’re not, because he likes football, and you don’t.’” He rolls his eyes. The other day, he says, Djalili asked him, “Have you ever wiped your arse on some toast?” as the character does in one scene. “No I haven’t done that! She’s made up all this stuff and people are going to think it’s me.”

He and Christie have one idea for a joint project that they might do one day when they are really old — “even if we’re not together any more” — based on their “really terrible” honeymoon in off-season Shetland. “Where it was dark 18 hours a day, and everything was dead and shut.”

In general, Lee is not keen on personal revelations in his comedy. He put a line in Snowflake about his son telling him off for breathing too loudly and agonised over it for ages. In the new work-in-progress show, he dangles a snippet of information about his early years in care before dismissing it.

“It’s other people’s lives, isn’t it? The circumstances leading to someone being put into care young . . . I probably come out of it a lot better than the people that were involved in that story. You don’t want to just drag them, without their consent, into the public eye. For what? Other people don’t seem to bother about that. I find the indiscriminate nature of people using other people’s lives and their personal stories quite shocking sometimes.”

Until recently, Lee had it all planned out — he’d perform a live show every two years until he was 60, then retire. He’s now 54 years old and his “Stalinist” ten-year plan fell apart in the pandemic. He’s now having to rush out Basic Lee faster than he would like because he doesn’t want to work next summer when his son is doing his GCSEs.

He still loves touring, and each time uses it as an opportunity to feed a new obsession. On his most recent tour, he sought out Victorian stained-glass windows in all the towns he visited. “Often the churches don’t even know they’re in there,” he says happily. He loves driving round the country, trying to get under the skin of the places he stops. “Touring comedians understand a lot more about where Brexit came from than any politician. You see the depletion of the towns . . .”

All of which is to day, he’s not going to stop performing at 60; in fact he thinks he’ll probably get better with age. “I did an interview with [the Teardrop Explodes singer] Julian Cope about ten years ago and he said, ‘Look, I know I’m a has-been at the moment. But if I can push through this I can become a legend.’ To keep going is better.”

Stand-up means survival to Lee. He thinks about it constantly. “If I’m really annoyed about something, I think, ‘I’ll slag them off on stage, that’ll show them.’ What do other people do? They kick the TV in, don’t they? Or go on Twitter? I don’t know how people that aren’t doing stand-up cope in their lives, really.”

Stewart Lee: Snowflake is on BBC2 tomorrow at 10.35pm; Tornado is on BBC2 on September 11. Basic Lee tours from September 6 to May 28 2023