It's getting hard to keep up. This week it was Bob Diamond claiming the peculiar amnesia of the powerful, protesting that he did not know or could not remember or did not remember if he once knew. Last week – or was it last month? – David Cameron was pleading similar forgetfulness before the Leveson inquiry, struggling to recall if he enjoyed a country supper with Rebekah Brooks every weekend or every other weekend, until his wife jogged his memory with a peek at the social diary. Before that, the Murdochs, père et fils, had suffered the same ailment of the mind.

Who will be next? Perhaps it will be those called to testify about the Libor scandal to the parliamentary inquiry established amid such acrimony on Thursday. Bankers will be summoned, of course, as well as a procession of officials and former ministers, thanks to Diamond's allegation of Whitehall involvement, hazily set out while he was not so much grilled as lightly toasted by MPs.

But bankers and politicians are the least of it. The bleak truth is that nearly all our key institutions have lost trust where they do not stand accused of outright corruption. Banks are in the frame now, as they have been since the crash of 2008. How astonishing to think that "bank manager" was once shorthand for dull dependability. How quaint it now seems, in the era of RBS and Fred Goodwin, that two decades ago, when political journalists sought to convey the flinty integrity of John Smith, they likened him to a Scottish banker. Now the term would be a rank insult.

The police's troubles go back a lot further – corruption in the Met was one of the enduring storylines of the 1970s. So maybe few are shocked by the reports of arrested police officers that now seem to punctuate every other morning bulletin: this week, the number of arrests linked to the Operation Elveden inquiry into bribery of police and public officials inched close to 40.

Meanwhile, the director of public prosecutions has signalled that the convictions of dozens more environmental campaigners could prove unsafe because a senior prosecutor may not have disclosed the truth about Mark Kennedy, the undercover cop who spied on political groups he had infiltrated as a member.

Of course, the reputation of the press has been blackened by the phone-hacking scandal and the rest of the grime unearthed by Leveson. MPs are still tarnished by the expenses scandal. The credibility of the EU is shredded daily by the failure of the eurozone. Corporations are tainted by the bankers' disease of excessive pay and their own corruption; the latest example reading like the plot of a John Grisham novel: GlaxoSmithKline has paid out $3bn after admitting it had marketed antidepressants for treatment of children and teenagers, even though the pills were not approved for that use, and that it had held back crucial data relating to a diabetes medicine.

One by one, institutions that people once depended on – banks, parliament, police, press – have been exposed as, if not legally corrupt, then rotten with greed. Football fans are learning that even their beloved teams are not immune: Manchester United supporters despaired this week as they saw their club move towards a flotation on the New York Stock Exchange, in an effort to pay back a chunk of the £423m debt that the Glazer family loaded on to United when they bought it seven years ago.

Dip into any radio phone-in or online comment thread and you can hear the fury all this is creating. It's easy to dismiss the current mood as hysteria, and the public's anger is certainly inchoate. The clear alternative ideologies around which collective rage cohered in, say, the 1930s are absent now. No one believes the masses are about to storm the palace. But the crisis of institutions is real.

Some will expend their energies looking for a single, root cause of this series of moral failures. It's tempting to conclude that the trouble began in the 1980s, with the triumph of the Thatcher-Reagan view that market forces – money – must always prevail, trumping all other values, including honesty and the common good. Thatcher's ministers used to say the pits had to close because they were "uneconomic", and damn the social consequences. Is it any wonder that Thatcher's children now ask themselves not whether a decision – to rig a banking rate, take a bung or raid the public purse – is right, but whether it's "economic"? If that's the question, then taking more money will always be the right answer.

Others will say 'twas ever thus, that corruption is a timeless part of the human condition. Either way, these concurrent crises of confidence in what were once pillars of our national life are having immediate political effects. One is a rise in the importance, and popularity, of the handful of institutions that do retain public trust, as people cling to the BBC, the NHS and, though some of us might regret it, the monarchy. (On the last of these, note how news of an 11% increase in Prince Charles's funding from the taxpayer triggered barely a murmur of protest.) The new director general of the BBC has to realise what a sacred trust he has inherited.

Second, the public's need for remedy is leading to an unlikely place. Believing that those they would once have turned to – police or politicians – are now themselves stained, many are turning instead to the judiciary. Judges used to be the butt of lefty jokes: this week a poll found 73% of us trust judges to tell the truth, compared to just 10% each for politicians and bankers. (Doctors topped the poll, with 85%.) Labour sensed the public mood when it demanded a judge, not MPs, inquire into the banking scandal, a demand to which Cameron will surely succumb eventually.

If this mood of radical disillusionment persists, it could shake up conventional politics. In Germany, the anti-establishment Pirate party has been polling in the mid-teens; here, Ukip is on the rise. Meanwhile, a referendum on Scottish independence looms: why would Scots vote to stay in a UK whose key institutions are deemed rotten?

Finally, Labour has to voice this anger. Ed Miliband did so early, with his assault on "predator" capitalism. He needs, though, to go further, not just so that his party can win back power – but for the sake of democratic politics itself. For if this rage does not find a peaceful outlet, it will find another way. But make no mistake: it will out.

Twitter: @j_freedland

• This article was amended on 11 July 2012. The original said that police had failed to disclose evidence about the undercover policeman Mark Kennedy. The director of public prosecutions said it was a senior CPS lawyer who may not have complied fully with disclosure obligations.