The Financial Conduct Authority, the City watchdog, said that CT Capital's failures meant some people missed out on PPI compensation.
The average redress payment was nearly £6,000, the FCA said.
CT Capital reviewed thousands of rejected complaints and changed its process after the FCA intervened.
PPI was designed to cover loan repayments when borrowers fell ill or were made redundant, but was mis-sold on a huge scale across the industry.
This led to a massive compensation programme involving many lenders.
CT Capital was the parent company of a group of lenders and loan brokers, together known as the CT Group. From January 2005 to October 2008, the CT Group sold 31,591 PPI policies, receiving a net figure of about £63m in commission as a result.
CT Capital was responsible for handling PPI complaints on behalf of the CT Group.
The FCA said that between May 2011 and November 2013, during which time it handled 6,669 PPI complaints, CT Capital failed to deal with claims appropriately, which resulted in customers missing out on redress payments to which they were entitled.
"Failing to handle complaints appropriately means that firms risk treating customers unfairly for a second time and it is important that firms get this right," said Mark Steward, FCA enforcement director.
"We have taken action against firms on numerous occasions and there is no excuse for firms continuing to get it wrong. We remain determined to ensure that firms put right the harm caused by PPI mis-selling and regain the trust of the public."
The FCA said that CT Capital revised its PPI complaint handling process with an external consultant and reviewed some 4,800 complaints, either previously rejected or underpaid. By January 2016, it had paid approximately £74m in redress arising from PPI complaints.
The parent company of a group of loan brokers has been fined £2.36m for the way it dealt with complaints about payment protection insurance (PPI).