Millions of people might switch banks if monthly or annual charges are brought in for using bank accounts, says consumers' association Which?
Would bank customers really object to new account charges?
In a survey of 1,022 people for Which?, 79% said they might move to another bank, while 73% thought current account charges would be unfair.
Banks have suggested they may bring in such charges if they lose their right to charge high overdraft fees.
A High Court case next year may rule on the legality of such fees.
Some 87% of those surveyed by Which? said the government should act to cap any new scale of current account charges.
"Consumers don't want to be charged for their current account and will vote with their feet if their bank introduces a monthly or annual fee," said Doug Taylor of Which?
"Our research shows that customers would support Government intervention to make sure banks don't overcharge," he added.
Since the 1980s, most banks in the UK have offered what is known as "free banking", a policy which is currently being investigated by the Office of Fair Trading in parallel to its scrutiny of overdraft fees.
"Free banking" means that normal current accounts are offered free of charge, so long as the customer is in the black or within a previously agreed overdraft limit.
The banks typically subsidise this by charging high fees when people go overdrawn without permission.
The issue of whether these fees are fair and lawful is now coming to a head after a huge and unprecedented consumer campaign during the past couple of years.
"UK banks offer the most cost effective and comprehensive package of current account services around and are keen to continue to do so," said Brian Capon of the British Bankers Association (BBA).
"We have always said there is a place for the current model of free banking and part of the reason for seeking the clarity of a court decision on bank fees is to defend this," he added.
The consumer campaign has seen hundreds of thousands of people forcing their banks to return hundreds of millions of pounds in overdraft fees.
The customers have claimed that the fees were in breach of the law on unfair penalty charges and threatened to sue their banks in the courts.
The issue has largely been put on hold until a test case early next year, involving the OFT, seven banks and one building society, attempts to decide whether the banks' charges are legal or not.
Whatever bank customers say now to the prospect of being charged while in credit, if there were an industry-wide policy of introducing annual or monthly fees, they might discover there was little choice between the banks.
But Marc Gander of the Consumer Action Group said more lawful and more transparent charging would be welcome.
"If we find millions of people do switch, then the banks might act more carefully," he said.
Inertia among bank customers means that people are still reluctant to move their current accounts, even if they are dissatisfied with the service they receive, because of the complications involved in moving direct debits and standing orders.
It has been estimated that only about 600,000 people do so each year.
This has been underlined by the experience of various former building societies which have converted to become banks in the past decade or so, but who have found it very hard to lure significant numbers of customers away from the High Street's big five.