It is a question of our age – arguably the question of our age – which links every story that is probably interesting you right now. It screams out of the allegations that a paedophile ring operated at Westminster. It is triggered again by the government's desire to rush through emergency surveillance legislation in the name of combatting terrorism. It is at the heart of the debate about the future of the NHS. It bedevils the arguments over independence for Scotland. It will be up front and central and decisive at the next British general election. Whom do you trust?

Comes an answer that is as popular as it is succinct: trust no one.

Trust me, I'm a banker. Don't think so. Trust me, I'm a doctor. Did you ever work at Mid-Staffs? Trust me, I'm from the intelligence services. And what did you have to do with rendition and torture? Trust me, I'm a police officer. How many innocent people did you shoot or stitch up to today? Trust me, I'm a bishop. Catholic or Anglican? Child abuser or investor in Wonga? Trust me, I'm a supermarket. How much horse is there in your burgers? Trust me, I'm from the newspapers. When does your trial begin? Trust me, I'm from the BBC. And what did you know about Jimmy Savile? Trust me, I'm a celebrity. How much tax are you avoiding? And were you mates with Rolf Harris?

Trust me, I'm a politician. Now, you're really having a laugh. I often hear it said that it was the expenses scandal that "destroyed trust" in politicians. The fleecing of the taxpayer by avaricious MPs certainly incensed voters and diminished the reputation of the political class, but parliamentarians were hardly laurelled with public esteem before that scandal erupted. Which prime minister was it who, on first entering Number 10, declared an ambition "to restore trust in politics"? Was it David Cameron? Gordon Brown? Actually, it was Tony Blair, which goes to show that what new prime ministers say when moving into office is a highly unreliable indicator – even a contrarian one. It also demonstrates that this crisis of trust is not a sudden phenomenon. It is no flash flood, but the product of decades of corrosion of faith in once respected institutions. What is often called the decline of trust is really an evaporation of deference. Where once there was a reflexive respect for authority and a willingness to give it the benefit of the doubt, there is now a default to distrust. Understandably when so many of those institutions have spectacularly betrayed our trust with their failures.

I recently asked a very senior Labour politician whether he thought that there were any pillars left standing, any of our institutions that still commanded public faith. After a long pause, he replied: "The Queen. I think people still trust her." That's a lot to leave on one elderly lady's shoulders.

Just when some thought this implosion of respect for key institutions could not get worse, worse it has got with the allegations of a "VIP paedophile plot" at Westminster and a decades-long conspiracy by "the Establishment" to cover up child abuse by senior public figures. For some, this is a spasm of mass hysteria. They caution against becoming overexcited by a lost dossier compiled long ago by a now dead Tory MP and rumour-mongering on the wilder shores of the internet.

Well, I like to think I am always on my guard against hysteria. But we can't put it all down to over-fevered imaginations. There is now too much evidence of sexual predators getting away with it in that era airily to dismiss the idea that it was also happening in the precincts of parliament. We already know – the case of the late Sir Cyril Smith – of one vile perpetrator. I'd be surprised to discover that there was a vast paedophile gang with tentacles gripping every nook and cranny of Westminster, but I wouldn't be at all surprised if it is shown that there were cases of offenders among MPs whose criminal depredations were hushed up by whips and other party managers for the usual self-serving reasons.

Faced with a storm about who did what when and who knew what when, the home secretary has done what all modern politicians do in these circumstances. Theresa May has gone into inquiry mode. She has announced two inquiries, which come on top of several other investigations, some still active, into sexual abuse. Whenever a scandal breaks, this is now the auto-immune response of politicians of all stripes: send for a judge. As well as the targeted investigation into what happened at her own department, the home secretary is establishing a second inquiry, huge in its scope, to examine everything that public bodies have ever done or failed to do about child abuse. It will range across the institutions, from the police to schools, from the NHS to the BBC, from the church to care homes to parliament itself. The epic sweep was designed to convince the public that David Cameron means it when he says: "No stone will be left unturned." Summoning an Olympian from the bench to preside was also supposed to instil further confidence.

Yet this traditional sedative for public outrage no longer works to calm the frenzy and bring politicians the closure they desire. Ever since Lord Hutton pronounced on the innocence of Tony Blair, we have become disinclined to place any more trust in judicial inquiries than we do in the politicians who commission them. Barely had the home secretary announced her inquiry than it was being denounced as an attempt to cover-up a cover-up.

There are two complaints, one specific and one general. The particular objection is to Lady Butler-Sloss as the chairwoman. The retired judge is the sister of the late Sir Michael Havers, who was attorney-general in the 1980s when the alleged abusers were not brought to justice. To the criticism that this creates an actual or perceived conflict of interest, there is a remedy: the home secretary can find a different judge. But it will be hard to locate a satisfactory answer to the more general complaint that no judge is a proper person to head this inquiry because judges are themselves part of the governing class. "The establishment cannot be allowed to investigate itself," argued yesterday's Times, the paper that is, or at least used to be, the noticeboard of the establishment.

The belief that all our institutions are involved in one giant, all-encompassing conspiracy against the public is now a very popular meme. In Great Britain, Richard Bean's play at the National that satirises the collusion of the press, police and politicians over phone hacking, the dramatist puts a speech about the establishment into the mouth of a tabloid news editor played by Billie Piper. "Twenty people who talk to 20 people. Democracy? Don't make me laugh." The audience respond with cynical, knowing guffaws. This is the sort of line that tends to win an easy cheer on Question Time. "The Establishment investigating itself. It will be a fix, a whitewash, a cover-up." Cue long and loud applause. Cue, soon afterwards, this thought. If we can no longer trust the judges, who then will be our investigators and arbitrators? Someone off the street chosen at random?

I guess in an ideal world we would elect the people we want as the invigilators and scrutineers of our public institutions. Perhaps we might call the head of that elected body something like prime minister. Of course, that would only work if we trusted them.

The paradox is that we still want to trust. The New York Times columnist, David Brooks, makes the interesting observation that we will now trust people we have never met with our money, our cars, our pets, even our homes. Peer-to-peer swapping and renting is booming on the internet. Sensible folk will take the precaution of checking the reviews and star ratings of the person with whom they are dealing, but that still involves putting trust in the recommendation of a stranger about the likely behaviour of another stranger. It seems we'd now rather trust an individual we don't know than a big institution that we have come to know much too well.

Unless you plan to hide alone in a cave, life can't be lived without trust. I go to bed at night trusting my neighbours not to burn down my house while I sleep. I get up in the morning and turn on the tap trusting the water company not to have poisoned the supply. We want to be able to trust banks, because we need somewhere to put our money. We want to be able to trust the media, because we need reliable sources of information. We want to be able to trust the doctor, the police officer and the judge. We even want to be able to trust our politicians. At least just a little bit. If our default assumption is that everyone who aspires to govern us only does so in order to lie to us and cheat us, then making meaningful political choices becomes impossible.

Trust no one is not a good motto for a happy life nor for a functioning democracy. Most of us intuit that. We mourn that we can't trust our governing institutions and yearn to see some restoration. There's a great prize here for someone in politics to win, if only any of them knew how to go about grasping it.