Much of this "old money" tradition survives today, perhaps best exemplified by such organisations as the small Fleet Street bank C Hoare & Co and, half a mile west, by Coutts & Co. However, private banks are increasingly turning their attention towards the newly wealthy: businessmen who have sold their companies; high-earning professionals; and beneficiaries of the explosion in City salaries.
David Maguire, head of marketing and sales at Lloyds Private Banking, says the number of wealthy Britons is growing much faster than the population at large. Warwick Newbury, the head of private banking at Coutts, estimates there are more than 2 million people who either earn more than pounds 100,000 a year or who have liquid assets of more than pounds 150,000. Only 100,000 of that 2 million use private banks, and about 30,000 of them are Coutts customers.
Kleinwort Benson Private Bank believes the financial needs of the "new money" higher-earners are very different from those of established clients, who have traditionally looked to generate an income from existing assets. Steve Reynolds, the marketing director, says: "The high-income earner is looking for a service that helps him or her to manage day-to-day income - to manage and pay down debts, and to generate assets for the future."
Kleinwort Benson's approach recognises that the first requirement of its customers may be a need to borrow. Hence its Mortgage Management Account offers clients a chequebook that allows them to draw down the equity in their property, as and when they need it. Subject to the normal income limits, the bank will allow clients to extend their loans to 80 per cent of the value of the property.
Most private banks promise personal service and generally seek to offer a comprehensive package through a single point of contact. Mr Newbury says the ideal private banking client is looking for "a good professional service all from one place - wills, mortgages, the core products of investment management, financial planning, pensions advice and, more and more importantly, tax. Everybody's working much harder than they used to, they just have not got the time to shop around."
Asset management, not fancy chequebooks, is the most important element of private banking. This is particularly true for the private banking arms of the clearing banks like Barclays and Lloyds.
Mr Maguire says Lloyds Private Banking has discretionary management (where it makes all investment decisions for you) over about pounds 6bn of client funds. Coutts, in the UK, has pounds 1.2bn.
Partly in recognition of the rising number of clients with high income but low assets, and partly in an attempt to broaden their appeal, some private banks are now willing to take on smaller investment portfolios. Coutts runs a portfolio service investing in unit trusts and investment trusts for clients with as little as pounds 25,000. Kleinwort Benson Private Bank will take clients with between pounds 50,000 and pounds 250,000 into its Select Service. More typically, Lloyds Private Banking seeks customers with investable assets of at least pounds 75,000. Barclays Private Banking does not set an entry threshold but Heather Maizels, a director, says the average client has more than pounds 1m under management.
Discretionary management tends to cost about 1 per cent a year, although the cost falls for larger portfolios. Kleinwort Benson charges 0.9 per cent on the first pounds 1m, 0.5 per cent on the next pounds 2m and 0.25 per cent on funds above pounds 3m.
Mr Maguire says some of the newly wealthy favour relative newcomers such as Lloyds Private Banking because of the forbidding reputation that Coutts (owned by NatWest) and C Hoare & Co have for catering primarily for the super-rich.
Henry Hoare, chairman of the 324-year-old bank, says it does no investment management for most of its 10,000 clients; it simply claims to offer a better banking service than the high- street banks.
He says: "We respond much more quickly. If something goes wrong with a standing order, we are better equipped to sort it out speedily and hopefully intelligently. We have better-trained staff and a higher ratio of staff to customers."