Individual savings accounts (ISAs) replaced PEPs and Tessas as tax-free vehicles last April, but the new system is far more complicated. Financial firms are certain that many savers have unwittingly loaded up on unauthorised accounts.
A spokesman for Abbey National said: "If a customer has a cash ISA with us, they might take out another at the Halifax. We make it clear you can only have one account per year but some people don't understand."
In 1999/2000 every adult can save up to pounds 7,000 in three different ISA accounts, one each for cash, stocks and shares, and insurance-based investments.
The biggest headache involves so-called "mini" cash ISA savings accounts run by banks and building societies. These appear to be normal savings accounts and have been heavily promoted by big names on the high street, with rates of interest of up to 6.5 per cent and no tax to pay. This compares with returns of around 4.5 per cent (after 20 per cent tax is paid) on the best ordinary instant-access savings accounts.
The savings limit on cash ISAs is pounds 3,000 this year but there is nothing to prevent individuals breaking this limit by opening several accounts with different banks and building societies and putting pounds 3,000 in all of them.
Small print asks customers not to sign up for a cash ISA if they have already taken an account out elsewhere, but providers have no way of tracking whether customers have ISA accounts with other banks.
A survey by the stockbrokers' trade association (APCIMS) last week suggested seven out of 10 people still have a poor understanding of the ISA rules.
Figures just released by the Treasury show that at least pounds 6bn poured into ISAs between 6 April and the end of June, double the amount paid into PEPs and Tessas during the same period last year. The Treasury believes most of this year's money has gone into bank and building society accounts.
The Inland Revenue is understood to be preparing guidance on how ISA accounts should be policed. Currently there is no way of telling how many people owe back tax until the tax year ends. Revenue staff will then match National Insurance numbers with complete ISA records to spot people who are bulk-buying - a task that could take months or even years.
A second "mis-buying" problem concerns the relationship between "maxi" and "mini" ISAs. Many investors who buy shares with their allowance have signed up to save as much as pounds 7,000 with a fund manager. Under the rules, if you sign for one of these maxi schemes you have used up your entire ISA allowance for the year.
Industry insiders believe there are thousands of people who forgot to cancel direct debits from PEP investments, and don't realise they have automatically been rolled into a maxi ISA or may have taken out other ISA savings accounts or stock market schemes.
A Treasury spokesman admitted there was no way of spotting any abuse of the system until next year but said the ISA rules would be reviewed after the first tax year ends.
Those who are found to owe tax will be forced to keep the first ISAs they opened and pay tax on the extra accounts.