Which? applied the charges of 21 different "free if in credit" current account providers to various different scenarios and found that people can rack up huge differences in charges, depending on how suitable the account is for their needs.
In the most extreme case it imagined, someone who regularly dips into an unauthorised overdraft could be £2,000 worse off a year than if they had switched to an account which better suited their needs.
The consumer group is pressing Chancellor George Osborne to use his forthcoming Autumn Statement to force banks to release information about how customers use their bank accounts to make costs easier to compare.
New rules were introduced in September which cut the length of time it takes to switch current accounts from up to 30 working days to seven and outgoing and incoming payments are now automatically transferred over by the new provider when someone switches current accounts.
The consumer group looked at a scenario whereby a current account holder had an average balance of £1,000, and took one trip to Europe during the year, making two £100 cash withdrawals and two £50 debit card payments.
The scenario also involved the account holder being overdrawn for several days of each month and having payments rejected as well as the interest the consumer would forego compared with if they had put their money in a best rate instant savings account.
Of the 21 providers it looked at in this scenario, Which? found that the Halifax Reward Account was the least expensive at a total annual cost of £329, which worked out £2,197 cheaper than the Bank of Ireland Clear Account Level 1.
The consumer group said that while Halifax's Reward Current Account is the cheapest it looked at for using an unauthorised overdraft, it was also one of the most expensive for authorised overdraft charges, but the information banks make available at present does not make it easy to compare accounts based on their needs.
Which? also looked at another scenario whereby a consumer has an average balance of £1,000, and also takes a trip to Europe during the year, making two £100 cash withdrawals and two £50 debit card payments.
This current account customer is using a £200 authorised overdraft for six days a month every month and this scenario also looked at the interest the consumer could have made if they had put their cash into a savings account instead.
It found that in this scenario, consumers could find themselves £120 worse off each year using the Classic Account from TSB, Lloyds Bank or Bank of Scotland than if they had used Clydesdale Bank or Yorkshire Bank's Current Account Direct.
Had enough of your bank? Earn £100 or up to 5% interest by switching to a top account
Which? executive director Richard Lloyd said: "With many households relying on their overdrafts to cope with the rising cost of living, we're calling on the Chancellor to force banks to release information so consumers can make sense of the way they use their account and choose the one that is best for them.
"Unless banks make it simple for people to compare the cost of running a current account, the new switching guarantee alone will fail to transform switching rates or significantly increase competition in banking."
Recent research by Which? found that going overdrawn on your current account can be as expensive as taking out a payday loan. The Government is clamping down on payday lenders' charges.
Eric Leenders, executive director of retail at the British Bankers' Association (BBA), said consumers should always shop around for the most suitable current account for their needs.
He said: "It's important that customers have the bank account that's right for them. This research shows that there is a real choice of current accounts on offer.
"The Money Advice Service has created an online tool that allows customers to compare the wide range of accounts. Earlier this year banks introduced a current account switch service that makes it easier for customers to change their provider.
"Research shows that most people are happy with their current account, but we would always recommend customers shop around for an account that's right for them."
The bank accounts you won't want to leave
The bank accounts that beat savings accounts
The account complaints the banks are trying to ignore