The Competition and Markets Authority (CMA) found measures so far to open up the market, dominated by Royal Bank of Scotland, Barclays, HSBC and Lloyds Banking Group, had not been effective enough.
It said key parts of UK banking lacked effective competition and failed to meet the needs of personal consumers or small and medium-sized enterprises (SMEs).
The CMA announced a consultation over its provisional decision to launch a full-scale 18-month inquiry, which could result in a series of reforms.
These range from enhancing information provided to customers to banning complex fees, capping overdraft charges and forcing banks to allow smaller rivals to use their branch networks or payment systems.
The CMA said going further and imposing so-called structural remedies such as forcing the break-up of banks could be expensive.
It cited the £1.4 billion cost to taxpayer-backed Lloyds Banking Group for hiving off hundreds of branches under the TSB brand under European rules on state aid.
But it said the problems facing the sector were so serious and long-standing it "cannot rule out the possibility that structural remedies may be necessary".
CMA chief executive Alex Chisholm said: "Competitive personal and SME banking markets are essential to households and businesses throughout the country, and to the success of the UK economy.
"However, our studies have found that, despite some positive developments, significant competition concerns remain which mean that customers may not be getting consistently good service and value from their banks."
Business Secretary Vince Cable welcomed the announcement, saying: "This is an issue that really matters for the real economy -- constraints on banking competition mean less choice for both consumers and small businesses seeking finance to grow."
It follows two studies in collaboration with City watchdog the Financial Conduct Authority (FCA) into the £8 billion personal current account market and the £2 billion SME current account and lending sector.
The CMA said concerns remained about competition not effectively serving customers despite measures to make authorising new banks simpler and faster, to make account-switching easier and to improve transparency.
The largest four banks account for 77 per cent of personal current accounts, 85 per cent of business current accounts and 90 per cent of business loans in the UK.
Annual switching among personal customers was low, with only three per cent switching each year, with the level at four per cent for banks' business customers. Satisfaction levels with the "big four" banks for personal current accounts were less than 60 per cent yet their market shares remained stable, it added.