There is only one composer who incites as much repulsion as he does reverence, as much adulation as he does suspicion. He is Richard Wagner, the composer of operas so ambitious that he decided the genre was insufficient to accommodate them. Instead he called them music dramas, and their gigantic explorations of Germanic legend were supposed to change the world.

But even Wagner could surely not have predicted just how operatic the saga of his own descendants would turn out to be. Unlike many Wagner operas, there has been some comedy among the Wagner clan, even if it is of a rather black sort. But there has also been much more than an average family’s share of deep duplicity, political scheming, and horrible human tragedy.

Never at any time has this turbulent family come under more scrutiny than they are now. For the first time in more than 40 years the Bayreuth Festival, established by Wagner to carry his artistic legacy, is under new management. Wagner’s 89-year-old grandson, Wolfgang Wagner, is infirm and has been forced to relinquish his leadership of the festival to two of his (formerly estranged) daughters, the half-sisters Katharina Wagner, 30, and Eva Wagner-Pasquier, 34 years her senior. Katharina was his chosen successor, groomed by years of working on stage productions at Bayreuth; Eva now returns as an outsider. Some say that this unlikely duo will inaugurate a new era. But neither should be resting comfortably after they have seen the provocative first episode in the final season of The South Bank Show. In Tony Palmer’s ferocious documentary, The Wagner Family, to be shown on September 13, dark revelations are piled on from the first minute to the last.

Here is Wolfgang Wagner’s mother, Richard Wagner’s English-born daughter-in-law Winifred, fondly recalling her close relationship with Hitler, conducted while she ran the festival and relied on his support: “I called him Wolf and he called me Winnie.” Here is Wolfgang’s own sister, Friedelind — who fled to America as the only member of the Wagner family not to support the Nazis — confidently recalling that the invasion of Poland was not only planned during a summer sojourn at Bayreuth but done so using Wolfgang’s geography textbook as a handy aid. Here is Wolfgang’s older brother, Wieland, actively involved in the running of a concentration camp just outside Bayreuth itself. And here is the postwar Bayreuth, supposedly free of Nazi associations, described as a police state by another rebellious Wagner, Wolfgang’s niece Nike, as she describes her uncle airbrushing out her father Wieland’s own contribution to Bayreuth.

Much of this unsettling testimony has already been thrown up by decades of scholarship, most recently Jonathan Carr’s excellent 2007 study, The Wagner Clan. But two things mark out The Wagner Family from the groundswell of incriminating evidence. The first is the hard-hitting allegation that the Wagner family knowingly aligned itself with Hitler’s movement from the beginning. The second is the charge that the family itself have been engaged in a persistent cover-up of the facts, whether to prevent interrogation about their wartime past or simply to keep power within whichever clique was in the driving seat.

Few could say that this investigation is an even-handed picture, but Palmer, a veteran of several penetrating (and invasive) studies of composers’ lives, is unrepentant. “They were in it up to their necks,” he says, unequivocally, “and they were absolutely in it from the beginning.” Worse, Palmer is also convinced that the family intend to keep the nastier bits of evidence firmly hidden away.

This summer Katharina announced that she did want the Nazi history of Bayreuth to be investigated. “There’s a shadow hanging over Bayreuth, and I feel a responsibility to try to get some clarity,” she said, adding that she wanted historians to carry out their investigations “independently of me and my family”. Palmer, though, is dismissive: his documentary includes a rare interview with one loyal Wagner relative, his grand-daughter Verena, who reveals how many valuable scores and documents were transported away from Bayreuth during the Second World War. Yet there are fears that this archive could contain the most incriminating evidence, and that it will not be released for inquiry.

Yet on this point — and, indeed, all the charges made in Palmer’s programme — the Bayreuth regime has been silent: neither Eva nor Katharina will speak further on the subject. Their defenders say that amends are already being made. The British opera director Keith Warner, who worked with Katharina on his Bayreuth production of Lohengrin between 1999 and 2005, believes that she is committed to coming to terms with the family’s past in the correct way — in the theatre, particularly her provocative 2007 production of Meistersinger (revived this summer), which explicitly confronted “Nazi” themes, including book-burning and mob rule. “The anti-Semitic legacy is truly absolutely appalling and I’m not arguing it shouldn’t be discussed,” Warner says. “But without being so specifically attached, what can you say about that issue that matters to us now? That’s what she’s trying to deal with — very brilliantly.”

Warner doesn’t deny the need to investigate the past. “If they are found to have really taken part in certain parts of the Nazi regime, like this concentration camp, then that must be shown, discussed, and outed.” But he also questions the need to hold one family’s behaviour up to such minute scrutiny. “You can’t make every single thing in these people’s lives linked to that. That’s the equivalent of what the Nazis were doing to those with Jewish origins.”

This, perhaps, is the heart of the debate: does a relentless mining of Wagner’s descendants’ transgressions really help or hinder the cause of Wagner? Shouldn’t it be his own dubious theories — expressed long before the birth of Hitler, let alone the rise of the Nazi party — that are pored over, alongside the music itself, rather than the deficiencies of his descendants?

“The Wagner family are Richard Wagner’s worst enemies, and they have been since the 1890s,” sighs Roger Allen, Wagner specialist and a Fellow in music at St Peter’s College, Oxford. “It was then that Bayreuth became not a place of experiment but a shrine, and as such took on the right-wing attributes which then made it a fertile ground for all kinds of right-wing nationalism.” All the nasty ideas, in other words, that are now indiscriminately ascribed to Wagner by those who would project history backwards.

And yet Dr Allen has never been more convinced that this history does need to be dissected. “To be able to move Bayreuth into the next era and make Richard Wagner’s art relevant to the 21st century these questions have got to be closed.” In other words, Wagner needs rescuing from the very family that twisted his legacy so badly, in the process polarising his audience up to the present day.

Palmer himself is no hurry to let the Wagners off the hook. “They are in effect the royal family of Germany. They do have a moral responsibility,” he insists. “They could have said ‘we knew, we were foolish, we said sorry’. I want a proper understanding of what they have done and the extent to which they are culpable.”

Should Katharina and Eva really open up that archive — the whole archive — let’s hope they are ready to deal with its contents.

The South Bank Show is on Sept 13 on ITV1

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