A watchdog wants an Office of Fair Trading investigation into the use of temporary headline interest rates to attract savers to cash Isas.
Tax-free Individual Savings Accounts (Isas) were introduced in the UK 11 years ago to encourage people to save.
The average interest rate stands at 0.41%, Consumer Focus said, with many banks and building societies "baiting" customers with short-term higher rates.
The British Bankers' Association (BBA) has criticised the watchdog's approach.
Consumer Focus has submitted a super-complaint to the trading regulator about the £158bn cash Isa market.
Consumer Focus believes that savers are missing out on interest of up to £3bn of interest a year, partly because it is difficult to switch providers.
The Office of Fair Trading (OFT) must now consider the complaint, and give a response within the next 90 days.
A BBA spokesman said Consumer Focus has chosen to launch its complaint "without any discussions with the banking sector".
"If we had been given the chance, we could have explained the work we are already doing with the regulator to help Isa customers," he added.
About 37% of UK households have a cash Isa. A significant proportion of those hold as much as is allowed in these accounts.
In April, the amount people can save in an Isa every year will rise from £7,200 to £10,200, of which half can be saved in cash and half, or all, in stocks and shares.
The end of the financial year usually brings a so-called "Isa season" with high levels of marketing by the various providers.
But Consumer Focus said that some offered eye-catching rates of more than 3% which dropped after a year to uncompetitive levels.
Other areas of concern included:
- A lack of clarity about interest rates for older cash Isas
- Obstacles to consumers' switching to another Isa provider
- Providers exploiting consumers' inertia and confusion by having similarly named accounts.
"At less than half of 1% interest the average Isa saver is getting a poor deal," said Mike O'Connor, chief executive of Consumer Focus.
"Of course, people could vote with their feet and switch to the 3% deals currently on offer, but we are concerned that the cumbersome transfer process and poor information provided by the banks inhibits doing this.
"There is evidence that very few people do actually switch their accounts. It beggars belief that in 21st century Britain it takes a month to transfer information and funds from one bank to another."
Adam Phillips, chairman of the Financial Services Consumer Panel, said: "Here is yet another example of banks being more interested in making money than in their customers getting a fair deal.
"It cannot be a fair outcome for consumers - or what the government wanted to achieve in providing this tax incentive - that people end up with little more interest from their tax-free account than they would get from an ordinary account."
The BBA spokesman added that from May "customers will be given advanced notification of any material reduction in the interest rate on a cash ISA, plus advance notice of the end of any bonus or introductory rate".
Super-complaints have been in the armoury of consumer groups since 2002. Examples so far have included complaints about bank charges, payment protection insurance, prison call costs, and doorstep lending.
In the Budget, Chancellor Alistair Darling said that the Isa limit will increase in line with inflation each year.