Millions of savers are getting a raw deal, particularly from the big High Street banks, the Financial Conduct Authority (FCA) has concluded.
In many cases, the interest rate on their accounts has been as little as 0.5% - the same as the Bank of England's base rate.
Savers should be given clearer information and helped to switch to better accounts, said the FCA.
But the City regulator stopped short of banning bonus rates.
Such rates operate for a limited period, and are used to tempt savers in.
The FCA also said that 80% of easy access accounts have not been switched in the past three years.
Furthermore, those who have older savings accounts tend to earn less interest than those who have opened them more recently.
The big High Street banks - "large personal current account providers"- are singled out for particular criticism.
The FCA said they attracted the most money into easy access accounts, even though they offer the lowest interest rates.
"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," said Christopher Woolard, the FCA's director of strategy and competition.
As a result of its investigation, the FCA is proposing:
The FCA will now consult on its plans, until 18 February.
Sam: 20th Jan 2015 14:34:00
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