The FSA has investigated packaged accounts sold by high street banks and forced at least one bank to refund customers after mis-selling.
In a recent review, the regulator found cases where accounts offering insurance policies and identity protection for a fee were poor value for money, costing up to £300 per year.
In other cases, customers were being sold packaged accounts despite already having adequate insurance, or being unable to benefit from the insurance offered by the account, the Daily Mail reports.
Some banks have been ordered to make changes with over seven million people currently holding packaged accounts.
In addition, some banks will now have to ask about the health of customers before selling them a packaged account.
Customers must be reminded in some cases of the cost and benefits of their account every year, and receive warnings if they already have existing insurance policies.
The FSA may follow the investigation with a consultation later in the year, the Mail reports.
A spokesperson for the regulator says: "We have stated before that packaged accounts can have real benefits for some customers, but they do not suit everyone.
"They are complex products and the FSA is carrying out analysis of this market, including consumer research, and is working closely with firms to see where and how improvements need to be made by the industry.
"Because of this work, changes are already taking place."
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