The offshore world is all around us. More than half of world trade passes, at least on paper, through tax havens. More than half of all banking assets and a third of foreign direct investment by multinational corporations are routed offshore. An impression has been created in sections of the world's media, since a series of stirring denunciations of tax havens by world leaders in 2008 and 2009, that the offshore system has been dismantled, or at least tamed. In fact quite the opposite has happened. The offshore system is in very rude health — and growing fast.

It is no coincidence that London, once the capital of the greatest empire the world has known, is the centre of the most important part of the global offshore system. The City's offshore network has three main parts. Two inner rings – Britain's crown dependencies of Jersey, Guernsey and the Isle of Man; and its overseas territories, such as the Cayman Islands – are substantially controlled by Britain, and combine futuristic offshore finance with medieval politics. The outer ring comprises a more diverse array of havens, such as Hong Kong, which are outside Britain's direct control but have strong links.

This network of offshore satellites does several things. First, it gives the City a truly global reach. The British havens scattered all around the world's time zones attract and catch mobile international capital flowing to and from nearby jurisdictions, just as a spider's web catches passing insects. Much of the money attracted to these places, and the business of handling that money, is then funnelled through to London.

Second, this British spider's web lets the City get involved in business that might be forbidden in Britain, providing sufficient distance to allow financiers in London plausible deniability of wrongdoing. Much (but not all) of the financial activity hosted in these places breaks laws and avoids regulation elsewhere.

The three crown dependencies in the inner ring are substantially controlled and supported by Britain but have enough independence to allow Britain to say "there is nothing we can do" when other countries complain of abuses run out of these havens. They channel very large amounts of finance up to the City of London: in the second quarter of 2009 the UK received net financing of $332.5bn (£215bn) just from its three crown dependencies. Jersey Finance promotional literature makes the point plainly. "Jersey," it says, "represents an extension of the City of London."

The 14 overseas territories, the next ring in the spider's web, are the last surviving outposts of Britain's formal empire. With just a quarter of a million inhabitants between them they include some of the world's top secrecy jurisdictions: the Cayman Islands, Bermuda, the British Virgin Islands, the Turks and Caicos islands and Gibraltar.

Just like the crown dependencies, the overseas territories have close but ambiguous political relationships with Britain. In the Caymans the most powerful person is the governor, appointed by the Queen. The governor handles defence, internal security and foreign relations; he appoints the police commissioner, the complaints commissioner, the auditor general, the attorney general, the judiciary and other top officials. The final appeal court is the privy council in London.

It is the world's fifth largest financial centre, hosting 80,000 registered companies, more than three-quarters of the world's hedge funds, and $1.9tn (£1.2tn) on deposit – four times as much as in New York City banks.

The third, outer ring of the British spider's web includes Hong Kong, Singapore, the Bahamas, Dubai and Ireland, which are fully independent though deeply connected to the City of London.

In the Caribbean, the modern offshore system traces its origins back to the time when organised crime took an interest in the US tax code.

When Al Capone was convicted of tax evasion in 1931, his associate Meyer Lansky became fascinated with developing schemes to get mob money out of the US in order to bring it back, drycleaned. A slick mafia operator, Lansky would beat every criminal charge against him until the day he died in 1983. Lansky began with Swiss banking in 1932, where he perfected the loan-back technique.

First he moved money out of the US in suitcases, diamonds, airline tickets, cashiers' cheques, untraceable bearer shares or whatever. He would put the money in secret Swiss accounts, perhaps via a Liechtenstein Anstalt (an anonymous company with a single secret shareholder) for extra secrecy. The Swiss bank would then loan the money back to a mobster in the United States and the money would return home, clean.

By 1937 Lansky had started casino operations in Cuba, outside the reach of the US tax authorities, and he and his friends built up gambling, racetrack and drugs businesses there. It was, effectively, an offshore money-laundering centre for the mob.

Lansky then moved to Miami and plotted to find his next Cuba, small enough and corrupt enough to be able to buy the political leadership, and close enough to the United States for the gamblers to come and go at will.

The Bahamas, the old staging post for British gun-running to the southern US slave states of the Confederacy, was perfect. Lansky set about making this British colony, now dominated by an oligarchy of corrupt white merchants known as the Bay Street Boys, the top secrecy jurisdiction for north and south American dirty money.

A quaint memo from a Mr WG Hulland of the Colonial Office to a Bank of England official in 1961, just as Lansky began major operations there, illustrates the uneasy nature of this encounter between the British upper classes and American organised crime: "We feel that this [lack of provision of an effective regulatory system] might be a grave omission, since it is notorious that this particular territory, in common with Bermuda, attracts all sorts of financial wizards, some of whose activities we can well believe should be controlled in the public interest."

London did nothing, and Lansky built his empire. Yet many locals were unhappy. In 1965 Lynden Pindling, a populist Bahamas politician, threw the ceremonial speaker's mace out of a parliament window in a dramatic power-to-the-people gesture. He was elected prime minister in 1967 on a platform that included hostility to gambling, corruption and the Bay Street Boys' mob connections.

Yet as it happened there was a reassuringly British place just next door, where the locals were far more friendly: the Cayman Islands.

Milton Grundy, an influential Caribbean offshore lawyer and author of several books on offshore finance, remembers first arriving in the Caymans. Cows wandered through the town centre, there was one bank, one paved road and no telephone system. In 1967 the Caymans published its first trust law, which Grundy drafted, and which a British Inland Revenue official subsequently said "blatantly seeks to frustrate our own law for dealing with our own taxpayers". Within just a few months Grand Cayman was connected to the international phone network and the airport was expanded to take jet aircraft.

Some have argued that Britain set up the offshore networks simply out of a short-sighted desire to find a way for its overseas territories to pay their way in the world. After the second world war, an exhausted Britain found that its empire, once a source of great profits, was becoming more expensive and difficult to run, as locals began to agitate for independence. But the evidence points to a different, more troubling explanation for Britain's decision to turn its semi-colonies into secrecy jurisdictions.

The archives tell a consistent story about how the tax havens grew: private sector operators working in a zone of extreme freedom began to call the shots, with little opposition from Britain and its inexperienced emissaries.

In the archives, two schools of opinion emerge within the British civil service. On one side sits the Treasury, and especially its tax collectors in the Inland Revenue, who virulently opposed tax havenry and found the Cayman Islands especially obnoxious. The US authorities were clearly highly vexed too, and the British Foreign Office broadly opposed havenry, though its position was more nuanced.

On the other side sits the Bank of England, the most vociferous cheerleader for the new arrangements, and its far less influential supporter, the British overseas development ministry, which seems unperturbed by the possibility that local tax haven activities might foster massive capital flight from developing countries elsewhere. Battle lines were drawn; the exchanges become vigorous and even acrimonious.

The Inland Revenue was especially alarmed, while their mandarin bosses in the Treasury showed some, but rather less, concern. They put together a working party, whose report in 1971 said Britain should, in effect, stop encouraging tax havenry in its overseas territories, which in the case of the Caymans had become, as one internal memo in London put it, "quite uncivilised".

A letter marked secret from the Bank of England dated 11 April 1969 gives a better sense of the forces driving the changes in the Caribbean.

"We need to be quite sure that the possible proliferation of trust companies, banks, etc, which in most cases would be no more than brass plates manipulating assets outside the islands, does not get out of hand. There is of course no objection to their providing bolt holes for non-residents but we need to be sure that in so doing opportunities are not created for the transfer of UK capital to the non-sterling area outside UK rules."

The Bank of England's main concern at this time was that the new Caribbean centres were weak points: sources of financial leakage outside the sterling area. So in 1972 Britain shrank the area to Britain, Ireland and the crown dependencies, excluding the new havens.

The year the sterling area shrank, the British officials working against tax havens disappeared from the archive files. Their replacements seemed unaware of the 1971 report and only discovered it in 1977, sitting on the shelf, unimplemented. Again they expressed concerns – and again nothing was done. History repeated itself within and between the departments, all in less than 10 years. And, each time, the Bank of England fought the tax haven corner.

"This is no tropical paradise," said Kenneth Crook, the newly arrived British governor of the Cayman Islands in 1972. "I could enlarge, in terms of a magnificent but mosquito-ridden beach; of a fairly new but rather ill-designed and sadly neglected house; of a pleasant but very untidy little town; of swamp clearance schemes which generate smells strong enough to kill a horse; of an office which will one day ere long collapse in a shower of termite-ridden dust."

But on politics, and the strange relationship between Britain and its little quasi-colony, his tone hardens. "Caymanians don't want independence," Crook wrote. "They don't want internal self-government either – they are very unwilling to trust each other with effective power … they quite well understand that the British connection gives them a status which they would otherwise not command."

Nothing of substance seems to have changed, as a senior Caymanian politician, who asked not to be named, explained to me in 2009. "The UK wants to have a significant degree of control," he said, "but at the same time it does not want to be seen to have that control. Like any boss, it wants influence without responsibility; they can turn around when things go wrong and say 'it's all your fault' – but in the meantime they are pulling all the strings."

This attitude of the locals towards Britain reassures investors, but the political bedrock underpinning the world's fifth biggest financial centre is Britain's role. If Caymanians gained full control, most of the money would flee.

While these changes were happening in the Caribbean, something similar was under way far closer to the City of London, in the crown dependencies. A constituent's letter forwarded and endorsed by Tony Benn, then an MP, to the then chancellor, Denis Healey, about a tax conference in Jersey, gives a flavour: "I am somewhat surprised to see a Mr Gent from the Bank of England giving advice on how to avoid paying tax. I wonder if this is really part of the Bank of England's duties? Mr Gent suggests that the Bank of England will not be prepared to pass on information required by the Inland Revenue! Does the UK Treasury have no control over the Bank of England? Surely Bank employees should not be working against government policy? And just what sort of arrangements and deals are made at these events 'behind the scenes'?

"It really is just a bit too sordid to be true."

As in the Caribbean, offshore banking blossomed here from the 1960s, when merchant banks such as Hambros and Hill Samuel opened for deposits.

Foreign travel was getting easier and more British expatriates opened accounts in Jersey, where the banks were reliable and comfortingly British, but where bank interest was untaxed and secret. Many did not declare their income to their countries of residence, often poverty-racked African nations, knowing they would not be caught.

Martyn Scriven, secretary to the Jersey Bankers' Association, described how Jersey's network grew. "The biggest business developer is client recommendation," he said. "The client will say, 'I'm happy, and I'd like to introduce you to my friend' – and you build it up like that. You get some seriously interesting people … someone who goes abroad as a rigger 20 years ago for Shell may now be in charge of the company's west Africa operations … We gather deposits from wealthy folk all around the world, and the bulk of those deposits are sent to London. Great dollops of money go into London from here."

As in the Caymans, Jersey has carefully protected the ambiguous relationship with Britain. Jersey's most senior public sector officials are appointed in London; its laws are all approved by the privy council in London, and Britain handles Jersey's foreign relations and defence, and the lieutenant governor represents the Queen.

As in the Caymans, Britain goes to great lengths to hide its control. And, as with the Cayman Islands, the relationship with the mother country reassures the wealthy and the financial services industry that Britain will step in if needs be, to protect the tax haven from external attacks. Their money is safe in Jersey.

This is an edited extract from Treasure Islands: Tax Havens and the Men Who Stole the World by Nicholas Shaxson, published by The Bodley Head this week, price £14.99. To order a copy for £11.99 visit www.guardianbookshop.co.uk.

For more info see treasureislands.org