It should be made easier for consumers to compare and switch between accounts in the 700 billion pound cash savings market where just six providers hold roughly two-thirds of all balances.
The regulator hopes that making switching faster and providing more timely information about pending changes in interest rates will spur account holders to shop around.
It is the latest study from the FCA which faces pressure to boost competition in financial services, a sector lawmakers say is too concentrated in the hands of the "big five" banks, HSBC, Lloyds, Barclays, RBS and Santander UK.
The five biggest providers pay on average "materially" lower rates on easy access savings accounts than smaller rivals, the study said.
The big players' 160 billion pound chunk of the market was earning an interest rate that was at or below the Bank of England record low base rate of 0.5 percent in 2013.
"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," Christopher Woolard, the FCA's director of strategy and competition, said in a statement.
Savings accounts are held by 93 percent of adults in Britain and include easy access accounts, fixed term bonds, regular savings accounts, and tax-exempt Individual Savings Accounts.
The watchdog put out several proposed changes to public consultation, including better information on interest rates and cutting the current 15-day switching time for cash accounts.
No time schedule for changes has been set yet.
Britain has already made it possible to switch bank accounts within seven working days to boost competition.
The watchdog had initial concerns about so-called teaser rates of higher introductory interest rates that tapered off but has decided not to ban them.
Nor will the watchdog force providers to offer all customers the same interest rate either, but they should inform customers better when rates are due to change.
(Reporting by Huw Jones; editing by Keith Weir)
By Huw Jones
