The white sands of Seven Mile Beach on Grand Cayman have long caressed the toes of the world's wealthiest financiers, who flock to this balmy spit to avoid the taxman's prying eyes.

But the world's biggest hedge-fund venue and fifth-biggest bank centre is now threatened, as the government of the Cayman Islands heads for bankruptcy — unable to pay its own staff and facing the prospect of introducing taxes as income from the world's shrunken financial system collapses.

But the situation is about to get worse after the British government, which has ultimate responsibility for the islands, last week refused to bail out the Caribbean idyll. It is not convinced the country will have the money to pay it back.

At the same time, hundreds of civil servants found that pension contributions and health insurance payments were missing from their pay slips. Contractors and government suppliers also had bills unpaid.

The leader of government business, William McKeeva Bush, begged the British government to borrow $310m (£190m) from banks. In a strongly worded response, Chris Bryant, a junior Foreign Office minister, has demanded the Caymans cut its borrowing and debt. And in a shockwave that will send tremors through the island's financial elite, Bryant even suggested that the tax haven introduce taxes.

"I fear you will have no choice but to consider new taxes – perhaps payroll and property taxes," Bryant wrote to Bush. "I understand, of course, that in so doing you will want to consider carefully the implications for Caymans' economy, including the financial services industry."

The wealth in the Caymans is staggering. Its hedge funds alone look after $2.3tn (£1.4tn), according to figures last year, and its GDP places it as the world's 12th richest jurisdiction, despite a population of only 51,900.

It made the Caymans a high-profile target as the global financial storm clouds broke. The Caymans were singled out by Barack Obama last year in his presidential campaign. It was also placed on a "grey list" of harmful tax jurisdictions by the OECD last April.

Chris Johnson, a British accountant who has lived there since 1968, is worried about his future for the first time in decades. "I would say I am pessimistic now. The island is in terrible trouble financially," he said.

The Cayman Islands, like most Caribbean island nations, is deeply divided socially and economically. On the one hand there are the ultra-wealthy – Microsoft's Paul Allen and golf champion Tiger Woods both moor their yachts there. On the other there are the native Caymanians, many of whom live in simple single-storey breeze block homes typical of the islands, with chickens and goats running about on scrub-like surrounding land. They are poor people who largely exist on the island to serve the wealthy in the hotels, private clubs and staffed households.

Cayman islanders say the previous government spent a huge amount of money upgrading the island's ancient infrastructure, betting it would be able to pay back a budget deficit of $67.5m as its financial sector continued to grow. But the global financial crisis has created a huge black hole in its budget.

The government charges financial institutions a licence fee based on employee numbers. But as banks and hedge funds shrink, income has declined. More seriously, US tourists cannot afford to visit. To fix the hole, taxes on personal income, financial transactions and tourism are being discussed. Most likely will be the introduction of a property tax.

Richard Murphy, of the campaign group Tax Justice Network, said: "Cayman is proving three things. The first is that tax havens are not sustainable: their business model is bankrupt. The second is that free-riding the tax system can't pay. The third is that international finance services that uses these places undermine the effective operations of states by denying them the resources they need to fulfil local electoral mandates."

One hedge-fund insider who lived in the Caymans said: "The heavy spending was well-intentioned because Caymans' infrastructure – schools, public health services, social services – are quite poor, given the assumed wealth of Grand Cayman. The devastating hurricane Ivan in 2004 didn't help … The problem was, the debt created to finance the capital expenditures was only affordable if the island's economy continued to grow rapidly. It was said many times that a US recession could lead to big problems."

And so it has been proved. The British government, which has ultimate responsibility for the Caymans, will hope that the islands' problems do not wash up on its shores.