This is what a potentially fatal mixture of delusion and complacency sounds like. Imagine it honked out in an upmarket accent, over drinks: "The thing about all this Leveson stuff is that nobody out there is interested. When you mention Rebekah Brooks, the only thing people know is that she used to be married to that bloke in EastEnders. That's about it."

Such were the rather haughty opinions of an unnamed cabinet minister, recounted a few weeks ago by the Observer's political editor Toby Helm. Of course, relatively few people can probably tell you what Craig Oliver does, or when Fred Michel's texts reached their peak of absurdity. But that's not exactly the point: the Leveson inquiry's abiding story, of a callow Westminster elite hopelessly in thrall to an increasingly disgraced newspaper empire, is inevitably oozing into the ordinary world, and the relevance of the wider story to public opinion will only grow. When some of the government's one-time friends and former aides start appearing in a real court, just you wait.

In the meantime, the inquiry's schedule for this week has the look of an extended political blockbuster: George Osborne, Gordon Brown, John Major, Ed Miliband, Nick Clegg, Alex Salmond and David Cameron, all called to explain their dealings with the press, and the Murdochs in particular. Cameron will appear on Thursday, and has plenty of questions to answer – though anyone interested in a much more formidable politician should also be glued to their TV the day before.

Salmond's standing in Scotland is built on the idea that he is not just a breed apart from Westminster politicians, but a self-confident grown-up in a world of mere kids – but as with the more pantomimic Donald Trump, the SNP leader's dealings with the Murdochs suggest he may also have slightly less heroic aspects. I was in Scotland just as the SNP's supposed omnipotence was called into question by Labour's surprisingly decent showing in last month's local elections: the Murdoch effect was undoubtedly in there somewhere.

What that should tell Westminster politicians is simple enough: that Leveson is relevant to the real world – but for now at least, its place in the public mind is less to do with who said what to whom than matters of perception. Certainly, a spectacle mostly glimpsed on evening news bulletins only reaffirms one of our era's most ingrained beliefs: that the political class is just that – a cloistered, incestuous bunch, whose obligations to courtiers too often outweigh the supposed demands of democracy. In that sense there is a salience to small but very telling human details: Tony Blair's anointing as a Murdoch godparent, Cameron and his "lol" texts, the fact that, according to Rebekah Brooks, her exit in the midst of those grim revelations about Milly Dowler's voicemail was met with messages of sympathy from "Number 10, Number 11, the Home Office, the Foreign Office".

The disgraced way of doing politics into which Leveson is peering is as much about culture as any decisions or policies. Yes, politics is cliqueish by nature, but what does it say about the post-Thatcher era that we have often seemed to be governed and spoken to by a single metropolitan gang, with the Murdochs and their circle at its heart? On this score, I always think of a party thrown less than a year ago by Elisabeth Murdoch and her husband Matthew Freud, mentioned at the inquiry a few weeks back. The setting was their 22-bedroom pile in the Cotswolds: among the attendees were James Murdoch, Rebekah Brooks, Michael Gove, Steve Hilton, Peter Mandelson, James Purnell, Douglas Alexander, David Miliband, Robert Peston, Mark Thompson, and Alan Yentob.

By way of a truly surreal symbol of much the same culture, consider also the events of a single week in August 2008 – when David Cameron met Rupert Murdoch on a yacht moored off the Greek island of Santorini, before the then leader of the opposition took his leave, and the same vessel made its way to Elisabeth Murdoch's 40th birthday celebrations on and around Corfu. There, events transpired that would lead to a heated controversy: Peter Mandelson famously dined with George Osborne, and also stayed in a nearby yacht owned by the Russian oligarch Oleg Deripaska, as a guest of the Swiss-based financier Nat Rothschild – who soon introduced Deripaska to the Conservatives' chief executive, Andrew Feldman. Meanwhile, the credit crunch was kicking in, the fall of Lehmans was only a month away, and Mandelson would be snugly back in government by October. Really: is it any wonder politics has fallen so far?

All this plays into the moment Leveson signifies: the lights suddenly being switched on, and politicians having to at least begin to account for themselves. Fortuitously, it arrives after levels of trust have been corroded by factors both specific, and more generalised: Iraq, the expenses crisis, the way that New Labour began offering an alternative to Tory sleaze and ended up mired in its own version; the fact that Cameron and Osborne seem to have managed much the same journey in only two years.

And it runs far wider than cosy relationships with the press, out into a web of special interests, and in turn into massively important questions of policy. Given that we are talking about a culture that ballooned under New Labour, one set of facts springs instantly to mind: that while the last government was increasingly glued to a world of lobbyists and high living, it did not seem even distantly aware of a snowballing housing crisis, the fact that the issue of immigration was being inflamed by so-called flexible labour markets, or any of the other issues that were corroding its support by 2005, and played their part in its awful thumping five years later. How could it, when it was part of such a rarefied culture?

So how to escape? Imagining a politics completely free of networks of power and influence would be fanciful, but to snigger and scoff at any suggestion that things could be better is to lose any real hope of probity – and simple dignity – ever coming back to the heights of public life. Everyone knows what needs to be examined: not just the ties that bind press and politicians, but party funding (note renewed headlines over the weekend about the Peter Cruddas affair), the role of special advisers, and a style of government that has come to favour back-slapping informality over proper protocol. Whether a professionalised political class can even start to grapple with its own failings is a huge question: that it will have to do so while the economy is in such a state doesn't exactly encourage optimism.

That said, between now and the autumn, demonstrating even the faintest understanding of post-Leveson politics would be easy enough. As a signal of good intent, one or all of the three main parties should cancel their annual conference (the Lib Dems, in fairness, have an internal democracy to see to, though they could at least scale their event down), turn their back on a schmooze-laden ritual that means absolutely nothing to the wider public, and redirect precious energy elsewhere. The bar is closed; the yachts are back in dock. For the first time in far too long, the real world calls.

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