High-street banks have long promised to go the extra mile for their customers, but none of them can purport to offer the kind of service private banks do.

Coutts recalls a story when a client dropped his wallet over the side of his yacht. One satellite-phone call later and the bank couriered out cards and cash to the next port he was going to. Then there was the diabetic client who got straight off an aircraft and into back-to-back meetings. When he finally checked into his hotel, there was nothing on the menu he could eat, so he called his bank – obviously – which duly sent a taxi there, complete with restaurant recommendations.

Private banks even send their clients' children on boot camps for offspring of the ultra-rich. AH Loder Advisers has an annual dog sled expedition across the Arctic. While billed as leadership training, these trips are as much about ensuring the children stay with the bank when they inherit.

But such service does not come cheap. Individuals have to have around £1m in investable assets before private banks will even deign to speak to them, though Coutts says this is flexible and it will "invest time to develop a client's potential, whether they be a lawyer or an entrepreneur".

Beyond these perks, private banks emphasise personal service. Where a retail bank will take a cursory glance at your credit rating, a private banker will ask about a client's family history and their "objectives for their wealth". Instead of a Mumbai call centre, customers will have the mobile number of their private banker, whom they can call at any hour of the day. It's hardly surprising; safeguarding the assets of so-called "high net worth individuals", who are often willing to pay a premium for secrecy, is highly lucrative. According to Tax Justice Network research, the top 10 private banks – led by UBS and Credit Suisse – had more than $6 trillion under management in 2010, up from $2.3tn five years earlier.

Much of the appeal lies in their discretion. Switzerland has long been at the heart of the private banking industry, with its tradition of secrecy dating back to 1934, when it became a criminal offence for employees to pass on information about clients' accounts to a third party, even government tax inspectors from other countries.

For years, governments turned a blind eye to their wealthiest citizens squirrelling away their riches in such tax havens. But since the global economic meltdown, cash-strapped governments are scrabbling around for revenue, and Switzerland has been one of the first places they have looked.

The UK government has struck a deal with the Swiss authorities to try and claw back at least some money from tax evaders. Under this deal, UK residents with undeclared assets in Swiss banks will be able to make a one-off, "clear the slate" payment of 21%-41% on their total assets and retain their anonymity. The Swiss will then levy a withholding tax on any future investment income and capital gains banked in Switzerland, set at 27%-48%. That compares with the top 50% rate of tax for funds kept in UK-based banks, due to be cut to 45% as of next year.

Tax expert Richard Murphy says this means those wealthy enough to transfer their assets are getting off extremely lightly: "It's extraordinary. It's legal to hide your money from HMRC now. You can complete a tax return and not put your income on it if it's hidden in a Swiss bank account. This is fundamentally wrong."

He says it also creates a perverse incentive for the wealthy to move money out of the UK. "And it gives no opportunity for the Revenue to go back to these people, most of whom have been tax evading for years," he adds. "This is rewarding past crimes."

A spokesman for HMRC says it is still illegal to hide money anywhere. He agrees that a UK resident does not have to declare income in a Swiss account if they agree to pay the one-off levy, but says that income will be subject to the withholding tax, which could end up higher than the rate they would pay in the UK. The deal was needed to crack open tax evasion cases, he adds, and could generate £4bn-£7bn in revenue.

Britain is very much a trailblazer in this regard. Only Greece and Austria have signed similar deals, while Italy is still in negotiations with the Swiss.

Germany has agreed a potential deal along the same lines as the UK, but it needs to be ratified by the German parliament and there is substantial opposition from individual states. That became clear last week when reports emerged that one state recently bought information from a whistleblower on potential tax evaders, which could blow a hole in the agreement.

North-Rhine Westphalia is said to have paid €3.5m (£2.7m) for a CD purportedly containing the names of around 1,000 Germans with assets in the Zurich branch of Coutts. Coutts has said: "Following thorough investigation, we have no evidence to suggest any such breach has taken place." This is not the first time such a CD has emerged. In 2010, several German states, including North Rhine-Westphalia, said they had bought CDs containing Swiss banking data, which led to thousands of Germans declaring their financial holdings to avoid going to jail.

The US has won more concessions, with a treaty allowing Washington to more easily identify US residents with undeclared Swiss bank accounts. It is also going after the banks themselves. The department of justice has charged Switzerland's oldest private bank, Wegelin & Co, with helping Americans hide more than $1.2bn (£770m) in secret accounts. It now has an ongoing investigation into 11 more Swiss financial firms and is discussing a settlement that could result in Swiss private banks handing over account data on thousands of US residents.

With banking secrecy increasingly under threat, private banks may have to organise ever more trips to the Arctic to keep their customers loyal.