(BBC) - Savers will receive a text message alert when their bonus introductory interest rate has expired, under new plans by the UK financial regulator.
Many people with savings accounts automatically move on to a poorer deal when the initial teaser rate is over.
Banks should alert customers to changes to interest rates or the maturity of a fixed-term account, the Financial Conduct Authority (FCA) said.
The plans follow an FCA investigation into the £700bn UK savings market.
"In a good market, providers should be competing to offer the best possible deal," said Christopher Woolard, director at the FCA.
"Consumers should expect the information they need to shop around to be clear and easy to understand."
In January, the FCA's investigation concluded that millions of savers were getting a raw deal, particularly from the big High Street banks.
It found that those with older savings accounts tended to be left earning less interest than new customers. In many cases, their rate was lower than the Bank of England's base rate.
The regulator is planning to name and shame that pay poor interest rates to longstanding customers.
The FCA had already ruled out banning introductory bonus interest rates, which is used to tempt savers, but now says that people should be "actively alerted" to changes in their rates.
Customers should be given clear information about the deal they are on, and be allowed to switch accounts with "the minimum of fuss".
Information should be clear to allow customers to compare accounts. This could come in the form of a switching box, which ranks the deal alongside industry norms.
Banks have argued that the low interest rate environment seen since the financial crisis is to blame for the low returns being offered.
"During this period banks have made it easier for customers to find the right savings product for them," said a spokesman for the British Bankers' Association, which represents the major banks.
"We always encourage customers to review their savings regularly and to shop around for a better deal. We will look at these suggestions from the FCA with great interest."
Campaigners believe banks could have done more, and have welcomed the FCA's proposals.
"For too long providers have increased profitability to the detriment of customers as their cash sits in accounts offering miserly returns," said Andrew Hagger, of Moneycomms.co.uk, who described the plans as "long overdue".
"Too often banks and building societies offer best buy deals for new customers whilst hoards of loyal savers on the back book are left with long forgotten deals paying next to nothing."
The plans will now go out to consultation, with rule changes earmarked for July 2016.
The FCA also wants customers with cash in Individual Savings Accounts (Isas) to be able to switch provider in seven days from January 2017.
