The ISA rules are much more complicated than the old PEP rules, and experts fear many more people will accidentally buy plans to which they are not entitled.
This may escape detection until the second application is audited by the Inland Revenue's Financial Intermediaries and Claims Office (FICO), up to four years after the second plan was bought.
Graham Bates, of Leeds-based independent financial advice firm Bates Investment Services, says: "There's much more likelihood that people are going to trip up on the ISA than they ever did with the PEP, because of the variety of ISAs."
One problem that looks certain to arise is that people will buy a cash Mini-ISA now - into which a maximum of pounds 3,000 can be placed in the first year - forgetting that for the rest of the tax year they may not hold any form of Maxi-ISA, with a pounds 7,000 overall investment limit.
If they then buy a Maxi-ISA from a second provider before 6 April next year, only a FICO audit is likely to reveal that rules have been broken.
Mr Bates says: "People won't hide it deliberately. They'll just forget that they've got a cash ISA, or describe it differently when asked."
Amanda Davidson of London IFAs Holden Meehan says: "People have enough difficulty remembering what year they did something in, let alone whether they bought a Mini- or Maxi-ISA. It will be a nightmare."
New research from Fidelity, aleading UK PEP and ISA manager, shows that only 22 per cent of potential savers understand you cannot hold a Mini- and a Maxi- ISA in the same tax year. "We are concerned that the Inland Revenue might see an increase in the number of people who have duplicated their ISA investment," says the company's Jo Roddan. For each fund manager, the gap between one FICO audit and the next could be as long as four years.
Justin Modray, an investment adviser at tax-free savings specialist Chase de Vere, recalls one client who inadvertently took out two PEPs in the 1996/97 tax year - one in October 1996 and the second on 4 April 1997. "He'd done a PEP before coming to us, forgotten to tell us, and then we did a PEP for him as well." The Revenue only picked this up 18 months later. Where invalid PEPs or ISAs are uncovered, the Revenue insists that the latest plan purchased be closed and taxed normally from day one.
Modray says: "If someone mistakenly takes out two PEPs in the same tax year, it may be some time before the Revenue realise. That can come as a shock."
Hardest hit will be big PEP or ISA savers who have already used up their annual capital gains tax allowance for the year (pounds 7,100 for 1999/2000), and so face a liability for CGT as well as income tax.
Janis Eat, an Inland Revenue spokeswoman, says the FICO audits carried out in 1998/99 revealed 43 PEP managers whose clients owed the Revenue a total of pounds 1m in unclaimed tax because of invalid PEPs. The audits also uncovered eight Tessa providers whose clients owed a total of pounds 400,000.
The bottleneck at FICO has been caused by foreign companies determined to beat the Government's 6 April deadline for the abolition of advance corporation tax credits.
Bill Dodwell, corporate tax partner at accountants Arthur Andersen, says: "Foreign companies which owned UK subsidiaries were under a lot of pressure to take dividends out and get their tax credits while they lasted. FICO got swamped with applications for tax credits, which are being processed now."
Ms Eat accepts that FICO is not meeting its target of replying to 80 per cent of all tax credit correspondence within 28 days, but claims this has not affected the unit's PEP and ISA work.
She says: "They have a cycle for auditing, and they're up to date. The team that goes out to do audits is different from any other FICO team, and so they wouldn't be affected by delays anywhere else in the FICO system."
What Are The ISA Rules?
l A maximum of pounds 5,000 can be placed into an ISA in any single tax year (pounds 7,000 in 1999/2000)
l Of this, you can place up to pounds 7,000 into equities, via a Maxi-ISA with one provider (pounds 5,000 after 1999/2000).
l Alternatively, up to pounds 3,000 cash in the 1999/2000 tax year and/or pounds 1,000 insurance can go into a Maxi-ISA, with the remainder going into equities. Thereafter, the ratio is pounds 1,000 cash and/or pounds 1,000 insurance and pounds 3,000 in equities.
l You can also set up Mini-ISAs with different providers. You cannot set up a Mini- and Maxi-ISA at the same time.
l If you do invest in a cash ISA, this limits to pounds 3,000 the amount that can be invested in equities.