The greatest danger of the rate-fixing scandal now engulfing the City of London is that it will be managed and defused in the usual way, and nothing will really change. Tuesday's forced resignation of Bob Diamond, the Barclays chief executive, follows well-worn procedures for dealing with crises that potentially threaten those in power: denounce the worst offenders, let a few symbolic heads roll, set up an inquiry under a safe pair of hands, and tweak the regulations to prevent a repetition of the most egregious misdemeanours.

That's been the pattern of the past few years as Britain's establishment has lurched from the disaster of the Iraq war to the disgrace of parliamentary expense fiddling and media phone-hacking (though in the case of Iraq, the only heads to roll were BBC executives and an army corporal). As for the banks that triggered the greatest economic crisis for 80 years, they have been bailed out and featherbedded, with only the loss of the odd sacrificial City baron to show for their reckless mayhem.

But we can't afford to allow such political dereliction again. The racket revealed around the rigging of the crucial Libor inter-bank interest rate – affecting $500tn worth of contracts, financial instruments, mortgages and loans – has underlined the scale of corruption at the heart of the financial system. It follows the exposure of the mis-selling of dodgy derivatives and payment protection insurance, voracious tax avoidance and last month's breakdown of the RBS-NatWest basic payments system.

It's already clear that the rate rigging, which depends on collusion, goes far beyond Barclays, and indeed the City of London. This is one of multiple scams that have become endemic in a disastrously deregulated system with inbuilt incentives for cartels to manipulate the core price of finance. Not only that, but the rigging has been public for years – it was first reported in 2008 – and no action has been taken until now.

That echoes the phone-hacking scandal, which erupted eight years after Rebekah Brooks told parliament News International was bribing the police and her admission was entirely ignored. On Tuesday Barclays sought to implicate Whitehall officials in its rate-rigging in 2008, and an angry Diamond, fighting for a payoff of over £20m, can be expected to go further when he appears before the Commons on Wednesday.

As they did with the Murdoch press, politicians who have abased themselves before the financial elite are now denouncing corrupt bankers and each other for failing to bring them to heel. David Cameron, whose party relies on City donors for more than half its income, wants a narrowly Libor-focused parliamentary inquiry to avoid the bigger picture and focus blame on New Labour's enthusiasm for "light touch regulation" in the runup to the crash.

Ed Miliband is rightly pressing for a much broader, Leveson-style public inquiry into the entire banking system. But the reality is that the whole political class embraced deregulated finance in the boom years. While Tony Blair and Gordon Brown pampered the banks, George Osborne and the Conservatives were demanding still less regulation, and even the Liberal Democrat Vince Cable, now the bankers' scourge, endorsed a financial "light touch".

This is yet another disgrace for the country's governing elites. The new revelation of corruption comes after the exposure of the deception of the Iraq war, fraud in parliament and the police, the criminality of a media mafia and the devastating failure of the banks four years ago. It could of course have happened only in a private-dominated financial sector, and makes a nonsense of the bankrupt free-market ideology that still holds sway in public life.

Political and business powerbrokers insist it's all a problem of leadership, bad apples and a culture that has gone awry. But such cultures are generated by structures and systems – and in the case of the City, deregulated short-term profit maximisation has as good as required them. It's certainly necessary to have a clearout of City bosses, prosecutions and wide-ranging inquiries, but only far-reaching change will clear this cesspit.

The financial system has already failed at huge economic and social cost. It has been shown to be corrupt, incompetent, rapacious and economically destructive. The City's claims to be an indispensable jobs and tax engine for the British economy are nonsense: the bailout costs of 2008-9 dwarfed the financial tax revenues of the boom years, which were below those of manufacturing even at their peak.

In fact, the banks are pumped up with state subsidies and liquidity that they are still failing to pass on in productive lending five years into the crisis. A crucial part of the explanation is the unmuzzled political and economic power of the City: its colonisation of Whitehall and public life, effective grip on its own regulation, revolving-door pull on politicians and civil servants, and purchase of political parties. Finance has usurped democracy.

The crash of 2008 offered a huge opportunity to break that grip and reform the financial system. It was lost. The system was left as good as intact, and even the part-nationalised banks, RBS and Lloyds, have since been run at arm's length to fatten them up as quickly as possible for re-privatisation (savage RBS cost-cutting lies behind its humiliating performance last month), instead of as motors of investment and recovery.

The rate-rigging scandal now offers a second opportunity to build the pressure for fundamental change. That's hard to imagine being carried out by a coalition dominated by the City-funded Tories, but Labour has also yet to break fully with its pre-crisis economic model.

Tougher regulation or even a full separation of retail from investment banking will not be enough to shift the City into productive investment, or even prevent the kind of corrupt collusion that has now been exposed between Barclays and other banks. As a report by Manchester University's Cresc research team argues this week, the size and complexity of the modern banking system makes it "near ungovernable".

Only if the largest banks are broken up, the part-nationalised outfits turned into genuine public investment banks, and new socially owned and regional banks encouraged can finance be made to work for society, rather than the other way round. Private sector banking has spectacularly failed – and we need a democratic public solution.

Twitter: @SeumasMilne

• This article was amended on 4 July 2012. The original misspelled Rebekah Brooks's name as Rebecca. This has been corrected.