Some 22% of consumers with these accounts, which bundle up a range of perks such as mobile phone and travel insurance in return for a monthly fee, said they either came across pushy sales practices or the deal later turned out to be unsuitable, according to the YouGov SixthSense research.
A regulatory clampdown to prevent banks and building societies pushing accounts which are not right for people came into force earlier this year following fears that people were being sold add-ons which turn out to be useless to them, for example travel insurance which the customer is too old to qualify for.
These accounts are held by around one fifth of UK adults and financial institutions must now check whether a customer is eligible to claim under each policy as well as sending annual statements so people can see whether the accounts are still suitable for their circumstances.
The Financial Ombudsman Service, which resolves disputes between consumers and financial institutions, recently reported seeing an upturn in complaints about current accounts, which was in part driven by people complaining they had been let down by a packaged deal.
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Despite the concerns raised in the research, only one in four people said they had done anything about it. One in 25 (4%) potential "mis-selling" victims said they had taken the matter up with the ombudsman. One in eight (12%) tackled their account provider about it and 7% applied to reclaim their fees.
The report also found that two-thirds (64%) of packaged account holders were happy with their deal and one fifth of these have claimed on an insurance policy included.
Simon Mottram, director of financial and professional services at YouGov, said that despite the £10 billion-worth of payouts which have been made as a result of the payment protection insurance (PPI) scandal, banks could still do a better job of explaining their products to customers and consumers should be questioning them more.
He said: "The vast majority of people with packaged bank accounts like them and feel they get good value from them. However, there are a sizable minority that believe they have potentially been mis-sold the products. The PPI scandal still casts a shadow over how consumers are sold financial products."
Some providers of packaged accounts have taken a step back from the market or signaled their intention to leave it altogether, while there have also been new entrants such as Marks & Spencer, which has been praised for tailoring its paid-for accounts to its loyal customer base.
The ombudsman has seen cases which include those from people who did not even realise they had a packaged account and the charge has shown up on their statement in an unclear ''administration fee''.
Firms buy insurance policies wholesale and offer them at discounted rates in the overall package, which can also make it hard for customers to compare costs with standalone insurance products.
More than 2,000 packaged account customers took part in the YouGov survey across the UK in May.