Older accounts, representing a significant chunk of the £700bn market, tended to have lower rates than those more recently opened, a study by the Financial Conduct Authority (FCA) found.
Following the study, the FCA wants to make it easier for consumers to compare accounts. Plans, which will be consulted on over the next month, also include reducing the current 15-day switching time for cash ISAs.
The watchdog said many consumers found it difficult to know what rate they were on or were put off switching by the expected inconvenience. It found 80 per cent of easy-access accounts had not been switched in the last three years.
FCA research concluded that simple changes in the way banks communicate to their customers could “significantly increase” shopping around.
It wants consumers to be given clearer information about how the interest paid on variable rate accounts may fall the longer they hold the account, and about how the rates they receive compare with alternative products.
The watchdog has stopped short of banning introductory bonus rates, as they may benefit some customers, but said it did expect providers to improve the way they communicate about interest rate changes and when the bonus rate expired.
Christopher Woolard, director of strategy and competition at the FCA, said: “In a good market firms should be competing to offer the best possible deal and consumers should have the information they need to help them shop around.
“We want to see firms making simple information much easier to find. More also needs to be done to reduce the hassle for consumers to switch their savings.
“The steps we have proposed today are designed to make the market more dynamic, working in everyone’s interest.”