The payday loan price cap is saving borrowers £150m a year and will remain in place until at least 2020.
Charges on payday loans were capped in 2014 to 0.8% of the amount borrowed per day.
The Financial Conduct Authority (FCA) said some 760,000 borrowers in the market are benefitting from the cap.
It also said firms are becoming less likely to lend to customers who can’t afford repayments and debt charities are seeing fewer clients with debt problems linked to short-term loans.
The FCA is now turning its attention to other forms of high-cost consumer credit including charges for unarranged overdrafts, rent-to-own schemes, doorstep loans and catalogue credit.
An investigation by the consumer group Which? in July 2016 found that some unarranged overdrafts cost more than a payday loan.
Which? found that some high street banks charged as much as £90 to borrow £100 over 28 days, compared to the maximum allowed charge of £22.40 on a payday loan.
The FCA said charges for unarranged overdrafts can be complex and therefore hard for consumers to understand.
The regulator is developing what it calls “tailored solutions to these issues” and will consult on them in spring 2018.
Lloyds Banking Group, which includes Bank of Scotland and Halifax, announced earlier this month that it will scrap all fees for unplanned overdrafts from November. Barclays customers have been unable to exceed their agreed overdraft limit since 2014.
Andrew Bailey, the FCA’s chief executive, said: “High-cost credit products remain a key focus for us because of the risks they pose to potentially vulnerable customers.
“We are pleased to see clear evidence of improvement in the payday lending market after a period when firms’ treatment of customers and their business models were often unacceptable.
“However, there is more that we can do, and this review is about identifying the areas where consumers may be suffering harm so that we can focus our efforts accordingly.
“In particular, the nature and extent of the problems that we have found with unarranged overdrafts mean that maintaining the status quo is not an option.”
Mike O’Connor, chief executive of StepChange Debt Charity, said it was disappointing that the FCA is waiting until spring 2018 to take action.
“The market is already showing signs of movement on this issue, so there is no need to delay vital changes that could address a major source of consumer detriment,” he said.
“The FCA is right not to loosen the payday loan cap and we have seen a marked fall-off in the number of people coming to us with payday loans problems.”
But he warned: “We need to ensure that people who need credit for essential costs are able to access products that are genuinely affordable and which don’t push them deeper into hardship.
“We believe that the government will need to provide major financial backing to support a low and no interest loan scheme.”