The City watchdog warned banks it is looking closely at the trend for lenders to pull back from offering current accounts.
Financial Conduct Authority chief executive Andrew Bailey said this was "an important focus" for the regulator, noting that banks regarded these types of accounts "as more expensive in terms of operational costs."
Bailey was speaking at the British Bankers' Association's (BBA) retail banking conference in London this week, after the Norwich & Peterborough Building Society revealed in January it would close all of its current accounts by the end of August.
A number of recent start-up challenger banks have also delayed launching current accounts.
Bailey described current accounts as part of the "essential" service banks provide. He said there are currently over 72 million personal current accounts in the UK holding deposits of over £1.5trn.
He said the FCA it will look at the role of current accounts in a wide-ranging strategic review of retail banks. The regulator added it was preparing to announce the results of its study of overdrafts and other short-term high cost loans, such as payday lending, this summer.
Bailey told the BBA that he knew many bankers were against "free-if-in-credit" current accounts – but he argued they did not in fact exist. He said: "Nothing in life is free – sorry to disappoint."
The head of the watchdog said because banks sold so many products, they can transfer costs across its range of services.
"The number of products creates more scope for less transparency in pricing and the assessment of costs," said Bailey. "There are always choices on how to allocate costs across products."
The regulator is concerned that as bank profit margins come under pressure from ultra-low interest rates, they are having to seek ways of compensating for the cost of current accounts by levying charges on other products such as overdrafts.