City regulator the Financial Conduct Authority has warned firms to comply with its rules and treat customers fairly.
It comes after Lloyds Banking Group admitted "issues" with the handling of customers' payment protection insurance complaints.
The FCA has previously said that it was looking into PPI firms' complaint-handling procedures and it plans to publish its findings later this summer.
An FCA statement said: "We expect all firms to comply with our rules and treat their customers fairly.
Firms know that PPI complaints must be thoroughly investigated and that appropriate action, where required, is taken promptly.
Our rules are very clear that firms are expected to learn from previous complaints. So if there are significant numbers of complaints coming in about the same thing, that is a clear warning sign that something isn't right.
The FCA said it is aware of the issues raised by TheTimes and it has been working with Lloyds since earlier this year to ensure they are resolved and customers' interests are properly considered.
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