Some banks are using "underhand" tactics to deter customers from challenging fees incurred for exceeding overdraft limits, Which? claims.
Bank charges are being examined by the Office of Fair Trading
A report by the consumer campaign group says some banks have threatened to close accounts or charged too much for statements needed for claims.
It comes as the Office of Fair Trading is preparing to report on bank fees.
The British Bankers' Association called the research "unfounded" and said bank account fees were "perfectly legal".
Doug Taylor, the personal finance campaigner for Which?, said: "In an attempt to avoid paying consumers what they are due, we have found that banks are employing increasingly underhand methods to avoid their responsibility to treat their customers fairly and refund the charges."
He said Which? believes banks have been over-charging customers who exceed their overdraft limit "for years" and "charging billions" in the process.
He told BBC Radio's Five Live that Which?'s research had found delays in answering letters and some banks closing accounts "if consumers challenge these charges".
"Many consumers, we know, have successfully challenged their charges, but we're a bit concerned that maybe some people are being put off by the length of time and the difficulties that they're facing," he said.
However, Eric Leenders from the British Bankers' Association (BBA) told BBC Breakfast that bank account fees were "perfectly justifiable and perfectly legal".
"We would say that if people feel that they, in turn, have been charged unfairly, they should always speak to the bank manager first.
"The information that's provided by Which? is unfounded and, in fact, could potentially be quite misleading."
The consumer campaign group said it heard evidence of several cases of banks charging between £3 and £5 per page for duplicate statements to start their claims.
The BBA said that all customers received statements of their account without charge - but that banks were entitled to charge an "appropriate fee" for duplicate statements.
Last year the top six High Street banks in the UK made an estimated £4.5bn from penalty charges, which include charges incurred for unauthorized overdrafts and bounced cheques.