Stewart Lee is in a good mood. “I’ve had a number one single at 52!” he tells me, beaming. Asian Dub Foundation’s Comin’ Over Here, which samples one of Lee’s old stand-up routines, topped the sales chart on New Year’s Day. It might be the first electronic dance hit to feature lyrics in Anglo-Saxon. (At one point, Lee shouts lines from the medieval poem “The Wayfarer”).

The most surprising thing about this – at least to anyone who knows him purely from his stand-up – is the idea of Lee being in a good mood. Petty and misanthropic, his onstage persona is rarely happy about anything.

It’s an act so convincing that not everyone realises it’s an act. “In Dublin, a journalist ran out and tried to file a report that I was having a nervous breakdown onstage, and was thinking that all these ghosts were attacking me,” says Lee. “I thought, yeah, result!”

There’s a reason the routine was so believable: each time Lee acted it out, he was remembering an actual experience. “My mother died 10 years ago, after quite a bad accident. I had to go back to work sooner than I would have wanted to. The first gig was at Wolverhampton. Afterwards, I always sit there at a little table and sell things to people, and my mum was about 4ft away from me in her brown coat that she’d always wear, with her handbag, and she said, ‘Hello’. I said, ‘I’ll just do this, I’ll be five minutes’ – and then a minute later I went, ‘Hang on, you’re dead!’ I think my subconscious needed to allow me to go back to work, so it created this figure.”

Lee comes across as something of a workaholic. He won’t be streaming his much-postponed touring show Snowflake/Tornado (“We spend our lives looking down blurred laptop screens. I don’t want to contribute to the weight of that”), but he’s itching to perform it to entertainment-starved crowds as soon as restrictions lift. “When music and comedy start again,” he says, “I think it might be just fantastic – like the jazz age!”

Lee’s latest turn, as an unlikely chart-topper, hasn’t come out of the blue. Since writing an Olivier-winning musical (2003’s Jerry Springer: The Opera) he’s dabbled in all kinds of left-field music. He’s made a jazz album, given performances of John Cage’s works and in July hopes to stage a “ritual” with avant-garde folkie Laura Cannell. On Isolation, an experimental album released last year, alongside serious contributions by members of Tangerine Dream is a track by The Stoke Newington Isolation Unit – which, it turns out, is Lee and his children, aged 10 and 13. Their song involves, of all things, a dulcimer. They had one lying around at home. “Bridge used to do an act as Charles II, and he had a dulcimer. She used to sing a song about different breeds of dogs on it,” Lee explains. “Bridge” is comedian Bridget Christie – or as Lee proudly calls her, “my wife, award-winning Bridget Christie”.

It’s easy to imagine a parallel universe in which Lee chose music over comedy. In ours, he is perhaps the most revered comedian of his generation: Stewart Lee’s Comedy Vehicle, his rule-breaking BBC Two series, was rated by The Telegraph as one of the five best stand-up shows of the past decade.

After dabbling in student sketch shows at Oxford, he got an early break writing for On the Hour (the 1991 radio comedy that introduced the world to Alan Partridge), and formed a double-act with Richard Herring who also wrote for the show.

How different things might be if Lee had stuck with Dust Harvest, the band he started in 1989. “The most stable line-up – of the four gigs that we played – was me, Al Murray on the drums, and Simon Oakes, who went on to be in alt-metal bands, and had a song on the soundtrack of Buffy the Vampire Slayer. He’s also the man responsible for setting the geography GCSEs.”

Does Lee ever think, “If only I’d stayed with the band…”? “I do, all the time. I think I might’ve been happier… Stand-up’s a very lonely furrow.”

What prompted this Sliding Doors conversation is a moment in Lee’s new film, King Rocker, in which comedian Frank Skinner tells the story of how, in 1976, he auditioned to be the lead singer in a punk band called the Prefects. Instead of Skinner, the band chose Robert Lloyd, who over the past 45 years has continued to make music (as Lee puts it in the film) “in the face of commercial and critical indifference”. It’s a stance Lee admires. “If I was who I aspire to be, I would be Rob,” he says. “But I’ve had the misfortune to find some way of monetising it.” Herring has said of his former partner: “In pursuit of integrity, Stewart is a man who seems prepared to cut off his face to spite his nose.”

It’s a comment that comes to mind when Lee tells me about his 2013-14 Comedy Central series The Alternative Comedy Experience, which gave many fringy acts a rare TV break. “A condition of it being recommissioned for the third series was that they wanted to change the title to Stewart Lee’s Alternative Comedy Experience.” He refused. It was cancelled. “If you want to look at it in modern terms, I don’t want to ‘dilute the brand’ by being spread like a thin lemon curd all over everything.”

King Rocker is not Stewart Lee’s King Rocker, but it may be his most personal work. The film’s director, Michael Cumming (Brass Eye, Toast of London), sees Lloyd as a father-figure to Lee, whose adoptive parents split up when he was four. Lloyd now lives in Wellington, Shropshire, the village where Lee was born. To make the film, the comedian had to return there for the first time since, as an infant, he was sent away to a children’s home. Being adopted “was weirdly an advantage in life in some ways,” says Lee. It secured him a place at “a minor public school on a grant for ‘orphans, waifs and strays’. So I got the sort of education that I never would have, had I not started out in care.”

Lee’s first foray into documentary-making is, on one level, a celebration of Lloyd and his post-Prefects band, the Nightingales, who seem to resist all attempts to celebrate them. But on another level, King Rocker is a love letter to a vanished world, “that world of John Peel sessions, early alternative comedy, going to little gigs in the backs of pubs, fanzines… The alternative comedy that made me want to be a comedian goes very much hand-in-hand with the music of that time.” Outside London, he says, “the only place where you saw the new comedy was when it crossed over with music – I saw Phill Jupitus opening for Billy Bragg in 1982.”

A eureka moment came two years later, when Lee saw the maddeningly repetitive, wilfully off-putting cult comic Ted Chippington supporting the maddeningly repetitive, wilfully off-putting cult band The Fall. “That really was it – I thought, I want to do this!” Stand-up, he realised, could be anything: “You didn’t have to be entertainment. You could be this tense, oppressive thing.”

King Rocker is on Sky Arts on February 6