The City of London Corporation is the oldest and arguably the strangest of all the many creatures in the menagerie of global finance. Despite its tremendous power and reach, it has flown underneath our political radar for a very long time. It is thrilling to see the London protesters dragging it into the light of day.

Some of the activists at St Paul's Cathedral issued demands on 31 October asking, in effect, for the corporation to be disbanded, the ancient offices of the Lord Mayor, sheriffs and the City police abolished and its unique voting system brought to an end.

The protesters are being called "anti-capitalists" - but theirs is most fundamentally a protest against an anti-democratic insider capitalism that is most virulent in the financial sector.

The anti-capitalist label risks putting them beyond the pale, consigning them to irrelevance in the public mind. The City of London Corporation represents this insider capitalism like nothing else on earth.

Few people know what the City of London Corporation is, let alone understand it. You can get lost in its website for hours and yet - like the eunuch in the brothel - still not quite grasp what is going on. Its operations are mostly not secret, but, before these protesters came along, who took the trouble to look into it?

It is perhaps easiest to think of it in two main parts. First, it is an almost 1,000-year-old local authority in the "Square Mile" of prime financial territory that lies at the geographical centre of London, fixing potholes and sending police officers to chase drunkards and petty thieves. The head of this authority is the Lord Mayor of the City of London, currently Michael Bear (not to be confused with the Mayor of London, Boris Johnson). When I went to see the corporation in January, it was this humdrum face that its representatives turned to me. We're just a minor local authority that gives loads to charity, they told me. Yet, unlike in any other local authority, corporations (40 per cent of them foreign) effectively vote in its elections - and they hugely outnumber the human beings. The Guardian's George Monbiot called this "plutocracy, pure and simple".

Its second role is different. It is a highly resourced lobbying organisation with an official role to support financial freedom and fight to keep London at the forefront of a deregulated global financial system. The Lord Mayor's central role is to push this message, lobbying at home and abroad. He hosts heads of state and government from around the world at the Guildhall and Mansion House. That is a very peculiar role for a local authority.

How powerful is the corporation? Let's be clear from the outset: it does not regulate or oversee financial markets in London. Its real influence lies in its tireless work behind the scenes to shape Britain's political and social consensus in favour of free finance. There is, as the protesters point out, a "remembrancer" (currently a tall, gentlemanly fellow named Paul Double), the City's official lobbyist in parliament, who sits facing the Speaker.

In the field of financial regulation and lobbying, the corporation's fingerprints abound. City Limits, a Demos report published in March 2011, which pushes a strong City line and argues that the recession was not caused by the UK's over-dependence on financial services, carries a short note from the former Labour minister Kitty Ussher, its author: "I am particularly grateful to the City of London Corporation for its financial support and helpful suggestions."

In 2008, when the government commissioned its inquiry into the financial crisis, four team members were from the City of London Corporation, including the Lord Mayor and two former lord mayors. It pumps out endless and widely reported research backing "competitive" (read "deregulated and low-tax") finance.

The corporation may be the best-resourced financial lobbying operation in the world. I've just been in the tax haven of Luxembourg, where spokesmen for the bankers' highly effective lobbying organisation Luxembourg for Finance told me it has an annual budget of about £2.5m. The City of London Corporation is far beefier. Its people told me that it has assets of about £3bn but I query that. It owns about a fifth of all the property in the Square Mile; my rough calculations suggest that its assets must be worth a lot more. We can't find out: it is exempted from all Freedom of Information inquiries beyond its role as a local authority.

In January 2000, Tony Benn called it "an offshore island moored in the Thames, with a freedom that many other offshore islands would be glad to have". Big Finance can lobby for itself but it cannot match the pomp and majesty summoned up by the Lord Mayor or the corporation's fortress-like constitutional role alongside parliament, impervious to some of the laws that govern the rest of us.

I cannot say whether or not the "Occupy" protesters should even have a set of demands. But if they should, then the strange and undemocratic plutocracy of the City of London Corporation is a fine place to start.

Nicholas Shaxson is the author of "Treasure Islands: Tax Havens and the Men Who Stole the World" (Bodley Head, £14.99)