The Financial Conduct Authority (FCA) said the market was causing significant harm to consumers.
New bank rules have been announced.
"Simply reforming the overdraft market is not the only factor at play here".
Bank overdraft fees are to undergo a major shake-up, which the United Kingdom financial regulator is calling the biggest overhaul for a generation.
Another change to the rules will see banks and building societies no longer able to charge higher prices for unarranged overdrafts than those which were arranged.
Banks have been criticised for using higher fees for unarranged overdrafts to help to subsidise other services.
Over half of banks' overdraft fees came from just 1.5% of customers in 2016, with people living in deprived areas most impacted.
The proposals include imposing the same prices for arranged and unarranged overdrafts, fixed overdraft fees, one standard interest rate for overdrafts, and requiring the lenders to advertise their overdraft rates.
Fixed daily or monthly charges for having an overdraft facility will also be banned.
"Vulnerable consumers are disproportionately hit by excessive charges for unarranged overdrafts.Consumers can not meaningfully compare or work out the cost of borrowing as a result of complex and opaque charges, that are both a result of and driver of poor competition", he added.
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In 2017 alone, United Kingdom banks and building societies made more than £2.4 billion in overdraft charges and fees, with around a third of this coming directly from unarranged overdraft charges and this is something that the FCA (as well as many consumers) see as unfair and immoral.
The FCA said research showed consumers wanted to see the cost of borrowing set out in pounds and pence alongside an April and interest rate.
Bailey said it was a radical set of measures that would make overdrafts fairer, simpler and easier to manage.
It has been estimated that it costs consumers around £5 per day when there is an unarranged overdraft outstanding, whereas with the new rules coming into effect, this should drop significantly to closer to 20p per day.
"Consumers can not meaningfully compare or work out the cost of borrowing as a result of complex and opaque charges, that are both a result of and driver of poor competition", said Mr Bailey.
It said the changes would make overdrafts simpler, fairer and easier to manage, protecting the millions of consumers, and particularly the more vulnerable ones, who use overdrafts.
The FCA is issuing new guidance, in order to reiterate that refused payment fees should reasonably correspond to the costs of refusing payments.
She said if people still end up paying over the odds the FCA should review the need for a cap.
"Overdrafts can provide a convenient way for customers to smooth their short-term cashflow, and there is a highly competitive market in the United Kingdom with over 96 products on offer".