Once, the banks would simply close an obsolete account to new business, leaving the savers already in that account to languish there. Since last July, however, the code has insisted that customers in these discontinued accounts are sent annual notice of the bank's other accounts and the (generally higher) interest they pay. But this clause applies only to accounts which are "no longer available to customers".
The idea was that savers in the discontinued accounts could then see that they would get a far better return elsewhere, and be able to change their account accordingly.
But the banks have already found a way round this. Now they leave the old accounts open. No one in their right mind would start such an uncompetitive account but - technically - they are still available to customers.
At the Consumers' Association, Neil Walkling says: "What tends to happen now is that the banks don't actually discontinue their old accounts - so that provision in the banking code doesn't apply.
"Say they're launching one of those new instant-access accounts that has limited withdrawals, but pays a much better rate of interest than the old instant-access account. There's no requirement for them to write to existing customers to tell them.
"That suits the banks because they don't have to pay the higher rate to all their existing customers."
Other scams operated by banks and building societies include hiding onerous conditions linked to apparently generous accounts in the small print.
In other cases, the product appears designed to catch savers out, such as Abbey National's postal account. This pays a bonus each quarter - but linked to the smallest amount in the account.
So, if the account held pounds 25,000 for most of the quarter but dipped to pounds 25 for one day, the bonus paid is on that smaller amount.