The financial watchdog, the FCA, says that millions of savers are losing out by letting their money sit for years in accounts with low interest rates.
It is calling for ideas on how to encourage switching between accounts and to make it easier to compare interest on offer.
Banks and building societies take advantage of people's unwillingness to shop around by offering higher rates to new customers.
The average interest rate on easy access accounts opened in the last two years was around 0.8%, but that the equivalent rate for accounts that were opened more than five years ago was less than 0.3%.
The FCA highlights the fact that providers come out with new versions of savings accounts with higher rates and leave loyal customers languishing on the old rates.
Many have attracted customers with bonus rates which only last a year.
But the watchdog also blames savers for not bothering to look for better deals.
It says they tend to keep their savings with the bank which provides their current account.
The average savings rate from leading current account providers is around 0.5%, but the equivalent rate offered by other providers is 1.2%.