The only impersonation I can do is my Jimmy Savile impersonation. This is not uncommon among people of my generation: if you were a child or a teenager in the 1970s and 1980s, Savile was quite possibly the most famous person in your entire world. His show Jim’ll Fix It was the most popular on TV with weekly audiences of 20 million. From Top of the Popsto his endless chat-show appearances promoting his relentless work for charidee, he was excruciatingly ubiquitous. Also, with his long, helmet–shaped, wig-like white hair, his garish tracksuits, bling jewellery and extravagant cigars, his catchphrases (‘Now then, now then’; ‘as it ’appens’) and his distinctive vocal mannerisms, he made it ridiculously easy to imitate him – almost as if, it occurs with hindsight, it was all part of his diabolical plan to suck us into his evil orbit and envelop our souls.

There was something Rasputin–like about Jimmy Savile – that power he had to hypnotise everyone around him, to make them laugh with him, indulge him and appear to be delighted by his company, despite the fact that he was so obviously the kind of weird, creepy guy you would have run a mile from if you met him in the street.

This is one of the things that makes Jimmy Savile: A British Horror Story so mesmerising. It doesn’t tell us an awful lot about Savile that we didn’t know already. But it’s still gripping because of all the archive footage of Savile doing his grisly schtick and being fêted and adored for it: a young, kittenish Selina Scott, for example, caught flirting with him outrageously on breakfast TV and looking for all the world as if she meant it.

But she didn’t – or so Scott assures us now, shown on the documentary looking appalled as she watches the incriminating archive footage. ‘They say the camera never lies but it does!’ she insists. And I believe her, though not quite for the reasons she gives. She has claimed in a newspaper article that: ‘There was immense pressure on young women in television to acquiesce to older men.’ Well sure but that misses the point that Savile wasn’t merely a beneficiary of old-fashioned sexism: he had the ability to manipulate (almost) everybody, male and female, young and old, obscure or famous, naive or hardheaded.

Look at the Duke of Edinburgh, for example. That man had fought in naval battles and was nobody’s fool. Yet there he is, caught on camera participating willingly in a charade whereby Savile acts as the Duke’s chauffeur from some event or other at Stoke Mandeville hospital and they drive off laughing their heads off. As a royal, he must have been painfully used to watching folk trying to ingratiate themselves and gain entry to the inner circle, and got very skilled at telling them where to go. So how come Savile managed to penetrate those defences? How come, for that matter, the similarly no-nonsense Margaret Thatcher fell for him?

Actually, that last question was answered quite convincingly by former cabinet secretary Sir Robin Butler. Savile’s remarkable skills as a fundraiser, Butler suggested, elided perfectly with Mrs Thatcher’s belief in the entrepreneurship and private charitable works which for her were key to weaning people off the teat of the state. Her ideological obsessions were the chink in her armour, which Savile spotted and gleefully exploited. Savile, as one of his former secretaries noted, was a very clever man with a remarkable talent for reading character.

However, like the serial killer who secretly wants to get caught he kept giving hints – in almost every interview he gave – that he was in fact a nasty piece of work with a closet full of skeletons. Time and again, he would bring up, unbidden, the subject of his relationships with girls (quite at odds with his deeply unerotic demeanour: he looked more like a freshly exhumed corpse than a viable sexual partner), or announce that if people knew his full autobiography he’d be facing a 15-year jail term. Being so frank about his crimes gave him the perfect alibi. Whenever nasty rumours surfaced, he could be excused on the grounds that he’d originated them himself, perhaps out of some perverse but harmless character defect whereby he’d run himself down for no good reason.

But perhaps his biggest get out of jail free card was his celebrity. Savile achieved such a pitch of showbiz eminence that he became untouchable, as one Sunday Mirror editor discovered when two girls from a remand home testified as to how they’d been abused by Savile when aged 13. ‘Who’d take our word against the word of someone so famous and establishment he’s even close friends with the royals?’ they asked – correctly, for the article never ran.

For me the most surprising revelation was the degree to which the Prince of Wales became infatuated with Savile, whom he considered a touchstone of rough-hewn wisdom and the authentic voice of the working class. The documentary had the receipts: handwritten letters on Prince Charles’s crested notepaper, pleading for Savile’s advice on this or that matter. Savile even put together a document in which he explained to the royals how to deal with crisis management. None of them appears to have been fazed by the idea of an ex-wrestler and nightclub bouncer with gangland connections and a dubious sexual reputation lecturing them on how to run their affairs. But then, nor did Broadmoor high security mental hospital when it decided to make Savile a live-in adviser with a grace and favour apartment. That’s the thing about Savile and why there can never be enough documentaries about him: everything about him is weirder than the weirdest fiction.