Swedish film-maker Jonas Åkerlund has been attracted to the wilder edge of rock’n’roll and I found myself grudgingly admiring his gruesome true-life death-metal horror thriller Lords of Chaos. So he was probably the right choice to direct this lavish docu-tribute to British postpunk legend Billy Idol, which combines a kind of humorous shrug at his outrageous excesses with something warmly sympathetic.

With that certain type of luck indistinguishable from talent, Billy Idol rode the tide of punk to new wave in the late 70s and early 80s, and then gambled on a move to the US; there he found fledgling 24-hour music video channel MTV, avid for content and always turned on by a self-destructive bad boy, which made him a big name. The film compares Idol to Elvis Presley, but there is something in that reflexive snarl-sneer that he used to do that has something of Eddie Cochran.

Idol himself, now 70 but looking good on it – especially considering that the last three words in the title are nothing less than the truth – looks back on his badass life and times in a cheerfully gravelly voice. He was always an insouciant TV interviewee, especially for the American journalists who loved to hear the naughtiness in the Cockney accent. “How are you?” asks one and Billy replies: “Mmm, yeah, I’ve had some very heavy sex since I’ve been here.”

But he abused drugs with religious devotion and intensity, which caused a near-fatal overdose in 1984 and then a second almost-as-bad episode in the late 80s in which he collapsed in a lift in a Bangkok hotel – to the horror of Mel Gibson and family who were trying to get into it. And then he almost had to have a leg amputated after crashing his Harley in Los Angeles, an accident he says finished off his budding movie career, although perhaps that might well have fizzled anyway. It’s a very enjoyable nostalgiafest.

• Billy Idol Should Be Dead is on Sky Arts on 26 March.