Cases like this are among those investigated by ITV's Find a Fortune series, as presenter Carol Vorderman and her team track down viewers' lost savings, legacies or pension policies. But you do not need all the resources of a television programme to be your own financial detective.
Halifax rationalised its own accounts at the end of 1995, in a process that switched many customers to new accounts with a different brand name and - in some cases - a new personal account number too. Alison Kellington, a Halifax spokeswoman, says: "When we got rid of all our obsolete accounts, we mailed all the people involved to tell them what we were doing. But it was an automatic transfer, because they were very much like-for-like accounts. If people find old passbooks, the best advice is to go to your local branch, and they'll be able to help you track them."
Where the bank whose name appears on the passbook has disappeared altogether, the process is not quite so simple. Bristol & West, for example, now holds money deposited by savers with the old Cheshunt Building Society, which Bristol & West took over in 1991. How are people who find an old Cheshunt passbook to know it is Bristol & West where they should pursue their claim?
Paul Vinnicombe, Bristol & West's savings product manager, says: "A lot of passbooks will have an address in them for the original branch and so on, and often there will be a link through. If you wrote to Cheshunt's head office, it would come to us."
Another route worth trying is your library, which may have a copy of the Bankers' Almanac, a book that lists name changes and liquidations. Where it is a vanished building society you want to find, the Building Societies Association may be able to help.
Even where problems with a dormant account are the customer's own fault, the situation can still be salvaged. "We have lots of accounts where people move and don't tell us," says Ms Kellington. "But those accounts still remain active."
Once you have placed money in a bank or building society account, that money and any interest it earns remains your property no matter how long the account is left dormant. Ms Kellington says colleagues tell of cases where Halifax accounts have been left untouched for as long as 40 years before the holder or one of his heirs has reclaimed the cash.
Sometimes, the problem is not that old accounts have been forgotten, but that money has been left languishing there when it could be earning a far better return somewhere else. Banks and other savings institutions tend to concentrate their competitive muscle on making sure accounts which can pull in new customers pay as high a rate as possible, leaving dormant accounts to drop far behind.
Here, finding out even what rate of return money in the original account is now earning could require some detective work. Bristol & West alone has more than 30 accounts which are closed to new investors, although still holding savers' money. All these accounts are now treated as if the money were in a Bristol & West Select current account, which pays interest at a paltry 0.1 per cent gross on even the largest balances. The bank's Postal Easy Access Plus account, its most popular product for new savers, pays a far more attractive 5.8 per cent gross.
Mr Vinnicombe says: "Most of the old accounts have a relatively small amount of money in them now, because people with large balances moved out some time ago."
For a free copy of the British Bankers Association's leaflet on dormant accounts and a standard claim form which can be used in any bank, call 0171-216 8801. For the Building Societies Association public information service: 0171-437 0655