It's the dark heart of Britain, the place where democracy goes to die, immensely powerful, equally unaccountable. But I doubt that one in 10 British people has any idea of what the Corporation of the City of London is and how it works. This could be about to change. Alongside the Church of England, the Corporation is seeking to evict the protesters camped outside St Paul's cathedral. The protesters, in turn, have demanded that it submit to national oversight and control.

What is this thing? Ostensibly it's the equivalent of a local council, responsible for a small area of London known as the Square Mile. But, as its website boasts, "among local authorities the City of London is unique". You bet it is. There are 25 electoral wards in the Square Mile. In four of them, the 9,000 people who live within its boundaries are permitted to vote. In the remaining 21, the votes are controlled by corporations, mostly banks and other financial companies. The bigger the business, the bigger the vote: a company with 10 workers gets two votes, the biggest employers, 79. It's not the workers who decide how the votes are cast, but the bosses, who "appoint" the voters. Plutocracy, pure and simple.

There are four layers of elected representatives in the Corporation: common councilmen, aldermen, sheriffs and the Lord Mayor. To qualify for any of these offices, you must be a freeman of the City of London. To become a freeman you must be approved by the aldermen. You're most likely to qualify if you belong to one of the City livery companies: medieval guilds such as the worshipful company of costermongers, cutpurses and safecrackers. To become a sheriff, you must be elected from among the aldermen by the Livery. How do you join a livery company? Don't even ask.

To become Lord Mayor you must first have served as an alderman and sheriff, and you "must command the support of, and have the endorsement of, the Court of Aldermen and the Livery". You should also be stinking rich, as the Lord Mayor is expected to make a "contribution from his/her private resources towards the costs of the mayoral year." This is, in other words, an official old boys' network. Think of all that Tory huffing and puffing about democratic failings within the trade unions. Then think of their resounding silence about democracy within the City of London.

The current Lord Mayor, Michael Bear, came to prominence within the City as chief executive of the Spitalfields development group, which oversaw a controversial business venture in which the Corporation had a major stake, even though the project lies outside the boundaries of its authority. This illustrates another of the Corporation's unique features. It possesses a vast pool of cash, which it can spend as it wishes, without democratic oversight. As well as expanding its enormous property portfolio, it uses this money to lobby on behalf of the banks.

The Lord Mayor's role, the Corporation's website tells us, is to "open doors at the highest levels" for business, in the course of which he "expounds the values of liberalisation". Liberalisation is what bankers call deregulation: the process that caused the financial crash. The Corporation boasts that it "handle[s] issues in Parliament of specific interest to the City", such as banking reform and financial services regulation. It also conducts "extensive partnership work with think tanks … vigorously promoting the views and needs of financial services." But this isn't the half of it.

As Nicholas Shaxson explains in his fascinating book Treasure Islands, the Corporation exists outside many of the laws and democratic controls which govern the rest of the United Kingdom. The City of London is the only part of Britain over which parliament has no authority. In one respect at least the Corporation acts as the superior body: it imposes on the House of Commons a figure called the remembrancer: an official lobbyist who sits behind the Speaker's chair and ensures that, whatever our elected representatives might think, the City's rights and privileges are protected. The mayor of London's mandate stops at the boundaries of the Square Mile. There are, as if in a novel by China Miéville, two cities, one of which must unsee the other.

Several governments have tried to democratise the City of London but all, threatened by its financial might, have failed. As Clement Attlee lamented, "over and over again we have seen that there is in this country another power than that which has its seat at Westminster." The City has exploited this remarkable position to establish itself as a kind of offshore state, a secrecy jurisdiction which controls the network of tax havens housed in the UK's crown dependencies and overseas territories. This autonomous state within our borders is in a position to launder the ill-gotten cash of oligarchs, kleptocrats, gangsters and drug barons. As the French investigating magistrate Eva Joly remarked, it "has never transmitted even the smallest piece of usable evidence to a foreign magistrate". It deprives the United Kingdom and other nations of their rightful tax receipts.

It has also made the effective regulation of global finance almost impossible. Shaxson shows how the absence of proper regulation in London allowed American banks to evade the rules set by their own government. AIG's wild trading might have taken place in the US, but the unit responsible was regulated in the City. Lehman Brothers couldn't get legal approval for its off-balance sheet transactions in Wall Street, so it used a London law firm instead. No wonder priests are resigning over the plans to evict the campers. The Church of England is not just working with Mammon; it's colluding with Babylon.

If you've ever dithered over the question of whether the UK needs a written constitution, dither no longer. Imagine the clauses required to preserve the status of the Corporation. "The City of London will remain outside the authority of parliament. Domestic and foreign banks will be permitted to vote as if they were human beings, and their votes will outnumber those cast by real people. Its elected officials will be chosen from people deemed acceptable by a group of medieval guilds …".

The Corporation's privileges could not withstand such public scrutiny. This, perhaps, is one of the reasons why a written constitution in the United Kingdom remains a distant dream. Its power also helps to explain why regulation of the banks is scarcely better than it was before the crash, why there are no effective curbs on executive pay and bonuses and why successive governments fail to act against the UK's dependent tax havens.

But now at last we begin to see it. It happens that the Lord Mayor's Show, in which the Corporation flaunts its ancient wealth and power, takes place on 12 November. If ever there were a pageant that cries out for peaceful protest and dissent, here it is. Expect fireworks – and not just those laid on by the Lord Mayor.