Despite ongoing efforts at reform, the Office of Fair Trading said comparing costs of current accounts is still challenging and people lack confidence in the switching process.
Though the watchdog has made new recommendations, it is minded not to refer the sector to the Competition Commission for further investigation, but will revisit the issue in 2015.
OFT chief executive Clive Maxwell said: "Personal current accounts are critical to the efficient functioning of the UK economy.
"Despite some improvements, this market is still not serving consumers as well as it should."
The OFT last looked into current accounts in 2008. Since then, it said, major banks have increased their share of the market, entry by new competitors remains infrequent and consumers still rarely switch providers.
And while people have saved up to £928 million a year from the fall in unauthorised overdraft charges between 2007 and 2011, the OFT said overdraft charging structures remain too complex.
It noted text alerts were helping consumers avoid unauthorised charges, but it wants banks and building societies to do more to promote this service.
There has also been encouraging feedback on the use of annual account summaries which detail what people have paid for their service and provide scenarios so customers know what they will pay if they exceed agreed limits.
The OFT said they would be of greater value if consumers had more consistent access to them.
It will also ask the Payments Council to look into the costs of enabling customers to transfer their bank account number.
The OFT hopes competition will improve with the sale of branches from both Lloyds Banking Group and Royal Bank of Scotland, while a new £750m automated account-switching service is to be launched in September.
British Bankers' Association chief executive Anthony Browne said: "We welcome the OFT's decision not to refer this issue to the Competition Commission and will continue to work with them to make further improvements."
Which? executive director Richard Lloyd said the OFT's "damning verdict" shows how badly people are still being let down by banks.
He said: "It's disappointing to see current account providers avoid immediate action by the competition authorities, but the banks are not off the hook.
"If the reforms under way do not quickly make a real difference to consumers, the whole of retail banking must be referred to the Competition Commission without any further delay."
A spokesman for the Payments Council welcomed the OFT's acknowledgement of the body's new account-switching service.