The rules would affect current accounts bundled up with a range of insurance policies, such as travel insurance, and other features such as overdraft facilities, music downloads and VIP lounge access.

According to the FSA, there is a risk that consumers may think they are covered by each policy, but later find they are ineligible to claim or that the policy is unsuitable in some other way.

Now being consulted on, the rules, which only affect non-insurance policies, will require banks and building societies to:

• Check whether the customer is eligible to claim under each policy and share that information with them

• Establish whether each recommended policy is suitable for the customer and alert them if some are not

• Provide customers with an annual eligibility statement setting out the requirements to claim each of the benefits under each insurance policy in the package which should prompt customers to check whether their circumstances have changed and whether the policies continue to meet their needs.

The FSA estimated one in five people now have these packaged accounts and the rules, if finalised, would come into effect from 31 March 2013.

Sheila Nicoll, FSA director of policy, said: “These products are often referred to as upgraded accounts but if you end up paying for an element you can’t claim on, it’s money down the drain.

“We are closely monitoring the promotion of packaged bank accounts and the new rules will make sure customers know what they’re buying and that they can rely on the product or have the limitations explained before buying.”

The FSA will also monitor the promotion of packaged accounts where monthly costs are advertised alongside yearly benefits.