The shock waves from the tsunami that has ripped through the financial system are hitting the discreet world of wealth management. This week, Swiss bank UBS, which has suffered particularly badly from losses in investment banking, showed how the damage to its reputation had a knock-on effect on its separate wealth management business. There was a surge of £24.4 billion in assets withdrawn by high net worth individuals in the third quarter. Other banks to be hit include Merrill Lynch, saved from collapse by Bank of America, which admitted to a net outflow of £1.8 billion from its wealth management division in the same period. Virtually no one has been immune from the turmoil, from billionaires Roman Abramovich and Lakshmi Mittal downwards. So it's no wonder that high net worth individuals, defined roughly as someone with £500,000 or more in liquid assets, are being more picky about where they keep their money.

We have seen with the abrupt collapse of Northern Rock and the Icelandic banks just how fast problems can snowball. Stories abounded a month ago that even customers of august private bank Coutts - everyone from Notting Hill property developers to fashion TV presenter Gok Wan - were considering whether to withdraw their money because of the parlous state of its parent company Royal Bank of Scotland. Customers' nerves were only assuaged when Gordon Brown announced his recapitalisation plan for RBS and other ailing banks.

Cath Tillotson, a partner at wealth management advisers Scorpio Partnership, says: "Some clients are undoubtedly moving their money. There is a 'flight to quality' in times of crisis, usually to a large bank. But what has changed in this crisis is that it is some of the large banks that have been suffering. So this is redefining what 'flight to quality' means."

Risk-averse investors, many of whom had already deserted property and the stock market, have been keen to put some of their cash on deposit. Beneficiaries include Santander, the Spanish owner of Abbey, and HSBC, with a big international customer deposit base. Also doing well are some of the smaller banks and boutique houses.

The venerable C Hoare & Co, the private bank headquartered on Fleet Street, is said to have been inundated with unprecedented levels of cash in recent months. Hoare is interesting because it is an independent partnership - the partners who run the bank are personally liable for the money on deposit.

While Hoare is rare in the UK, Switzerland has more than a dozen private banks such as Pictet, Lombard Odier Darier Hentsch and Julius Baer that operate as partnerships. "Some of these Swiss private banks have been doing incredibly well," says Tillotson of Scorpio. She argues that even the troubled heavyweights of Swiss banking, UBS and Credit Suisse, look well-capitalised now that they have got the financial backing of their national government.

But change does not always happen fast in wealth management: First, high net worth individuals often have longstanding relationships with their private bank or advisers. "It is quite complicated if you have a portfolio managed by a firm, it's a cumbersome process to move it," explains James Anderson, chairman of Tru-Est, which publishes the authoritative Private Asset Managers (PAM) directory.

And then there is the question of trying to identify a wealth management firm that might do a better job. "There are very few firms out there that have satisfactorily managed to look after their clients' capital," says Anderson. "People will wait a while before moving their money elsewhere. They will think very carefully about it."

Plainly the key reason for any decision to move around assets is personal circumstances. Some long-term investors can afford to sit on their hands and wait for the upturn. However, others may have pressing reasons to move - even if it means taking a big loss.

In some cases, it still has not been easy to withdraw funds. Ailing insurance giant AIG and a number of leading hedge funds have suffered such big outflows of assets during the turmoil that they have blocked some investors from pulling out money immediately.

Investors who have got their fingers burnt are now far more wary. "This is a people business, it's about building relationships and building trust," says Anderson of Tru-Est. "The big challenge for the big institutions is that they have looked at wealth management as a distribution channel to sell their financial products instead of focusing on that personal relationship. They need to be focused on wealth protection rather than just wealth management."

There is one final point. Despite overall losses at UBS, the wealth management division made a profit of £995 million in the third quarter. It still looks after £1 trillion of assets - so a net withdrawal of £24.4 billion by investors in the last quarter doesn't look quite so bad. Likewise, Merrill's wealth unit made pre-tax profits of £484 million in the quarter and has £937 billion under management.

So recession may be in the air, but wealth management remains highly profitable.