In 1988, when two City financial whizzkids, Stephen Partridge-Hicks and Nicholas Sossidis, invented "structured investment vehicles", they inadvertently ignited the fuse that blew up the world's financial system in the Crash of 2008. Their company, called Gordian Knot, helped banks devise ingenious ways to hide their extravagant risk-taking by creating off-balance-sheet companies. They had created a Gordian knot all right - a system of financial mechanisms so complex that no one could unravel what was going on.

This past week Gordon Brown, a latter-day Alexander, tried to cut the Gordian knot, but he may have simply set the public finances adrift on a sea of debt. The state has exposed itself to the billions of pounds in liabilities held off the balance sheets of Britain's delinquent banks. This is the world of shadow banking.

The stock market crash early this month was largely a result of panic selling in this shadow banking system of structured finance. Hedge funds and, to some extent, private equity companies are having to liquidate billions in assets as their business models collapse under the weight of falling share and house prices. Until these losses work their way through the system, the British economy remains in intensive care.

The madness of the shadow banking system became apparent over a year ago when Northern Rock was nationalised, but regulators ignored the implications. The Treasury minister Yvette Cooper discovered to her dismay that Northern Rock didn't own half of its own mortgages: £50bn had been hived off to a Jersey-based company, Granite, registered as a charity benefiting Down's syndrome children in the north-east of England. Needless to say, the charity didn't get any cash - this was a special-purpose vehicle that allowed the Rock to trade in complex securities without having to meet the stringent capitalisation requirements of a normal bank.

But it wasn't just the Rock. Most banks and other financial institutions did exactly the same, setting up "orphan companies", often under charitable trusts, that did not appear on their published balance sheets. This is one reason why such apparently well-capitalised and solvent institutions as Royal Bank of Scotland collapsed so suddenly. Their true liabilities had been hidden for years in the shadow system while they made huge profits from lending.

How did they get away with it? If you or I set up fictitious offshore identities to evade tax and conceal high-risk financial activities, we would end up in jail. But the regulators turned a blind eye, partly because they didn't fully understand structured finance, and partly because the government believed that it must be a good thing, as it generated so much profit and tax revenue. This was the regime of "light-touch regulation" of the City that turned the British economy into a cross between a Liechtenstein tax haven and a giant hedge fund.

The claim about SIVs, as with hedge funds and private equity companies, was that bankers had found ways to "abolish" risk through complex financial engineering. Typically, they packaged up long-term debts, usually residential mortgages, sealed them with credit default swaps (theoretically insuring the risk of loan default) and sold them as securities. It was a unique combination of self-delusion and financial manipulation, ultimately premised on the notion that house prices could never fall. The financial engineers were often mathematicians who possessed brilliant minds but were devoid of common sense.

Like medieval alchemists, hedge-fund managers claimed to possess a mysterious secret formula, called "alpha", which allowed them to make profits in any market, bull or bear, through speculative activities such as short selling. In fact, their innovative "alpha" was largely based on boring old debt, cheap money. Private equity companies used easy credit to launch leveraged buyout raids on FTSE companies. Money was so cheap that you could buy billion-pound firms by putting up less than a hundred million of real capital - the rest was borrowed from banks eager to hand on the huge amounts of credit they were generating through their shadow banking system. It was a hell of a party, until it ended.

The Brown package is imaginative, comprehensive and deservedly praised – not least by the Nobel Prize-winning economist Paul Krugman – but it is also a hell of a risk

The exploding market in credit default swaps was an integral part of this world of fantasy finance. CDSs are like insurance policies taken out on the possibility of a company defaulting on its debts. It is rather like taking out insurance on your neighbour's house burning down - only this is multiplied by thousands of other speculators also betting on your neighbour's house burning down. The trouble was that no one actually knew who was liable if and when the house did burn down - until one investment bank did burn down. The collapse of Lehman Brothers triggered $400bn worth of credit default swaps. Since then, all the parties to these unregulated derivative contracts have been trying to avoid the losses from the conflagration of Lehman bonds.

The CDS market had grown from almost standstill to $62trn in seven years. Swaps were traded as if they were bonds, meaning that they turned into another source of credit and leverage. The global market in financial derivatives as a whole, of which CDSs are a part, has grown to more than £500trn - a huge black cloud hanging over the world financial system.

The truth is, no one knows what's out there. The British government is in the process of spending £500bn to find out through nationalising the likes of Royal Bank of Scotland and underwriting all new bank debt. The Brown package is imaginative, comprehensive and has won widespread praise - not least from the Nobel Prize-winning economist Paul Krugman - but it is also a hell of a risk. The enormous losses of the shadow banking system could now find their way on to the public balance sheet.

There is a huge deleveraging under way, which will bring trillions in losses across the world banking system. The hedge-fund industry is disappearing before our eyes as worried investors pull their money from these vehicles that pro mised never to lose. It is expected that the industry will halve in value to roughly $1trn, but its leveraged liabilities will be much larger than that.

If, as expected, British property slumps by 35 per cent, that will mean another £1trn or so of value removed from the financial system, further undermining the value of all those mortgage-backed bonds in the SIVs. Even after the post-bailout rally, the UK stock market has lost a trillion or so this year. Who pays? Well, pension funds will absorb many of the losses. They are estimated to have lost £150bn so far, but the true figure will be much higher. The 2.5 million homeowners who will be in negative equity if the 35 per cent fall in house prices takes place will also be paying debts for many years. Sovereign wealth funds that invested in British banks and equities will find themselves out of pocket.

But an awful lot of money is going to land on the public purse. The shadow banking system is an imponderable black hole of financial loss. According to the Institute for Fiscal Studies, the liabilities from RBS alone could add £1.8trn on to the public debt, taking it to £2.5trn. Britain's GDP is only £1.4trn. These are terrifying numbers. Be in no doubt: if all the liabilities of the UK banks fell on the state, Britain could find itself in the same predicament as Iceland. Our economy is actually very similar, only on a much larger scale.

Sorting out the shadow banking system, assessing liability and clearing out the debt will be a huge task for the British government and people. It will take great ingenuity and international co-operation of a kind never seen. Gordon Brown showed political courage in cutting the Gordian knot. Now he faces the larger task of cleaning out the Augean stables.