The Financial Ombudsman Service will conduct an independent review following accusations that some consumers' claims were not decided correctly.
The move follows an investigation by Channel 4's Dispatches into the service.
The programme suggested some staff with inadequate training or knowledge were making decisions on complaints.
It also raised concerns that pressure to resolve cases quickly may have led to banks being wrongly favoured.
The review was announced after Nicky Morgan, who chairs the Commons Treasury Committee, wrote to Caroline Wayman, chief ombudsman and chief executive of the service.
Ms Morgan said it was "troubling" that some cases may not have been decided correctly.
The independent review must consider the service's approach to decision-making, the assurance process, and the causes of low staff morale, the MP said.
"The review should be demonstrably independent, all findings of the review should be published, and the committee will expect to take evidence from the reviewer."
More small businesses get access to Financial Ombudsman
Schwarzenegger hired to highlight PPI claims deadline
Ms Wayman said the service's board would appoint an independent person to "better understand and address the concerns raised" by Dispatches.
"We feel very strongly that the concerns voiced in the programme do not give a fair impression of the Financial Ombudsman Service when seen against the overall breadth and context of our work," she said.
The service has faced a huge workload in recent years following the payment protection insurance (PPI) scandal.
Since 2010, when the service began handling large numbers of PPI complaints, Ms Wayman said it had found against banks in about two-thirds of cases.
How to make a PPI claim
More information on PPI and how you can claim is available on the FCA website.
A free phone line, managed by the FCA, can be called on 0800 101 8800.
Various templates are also available to download, along with guidance on claiming, on websites such as Which?, MoneySavingExpert, and Resolver.
Responding to a question from Ms Morgan about whether the ombudsman could reopen past cases, the chief ombudsman said it could only do so if "material new evidence subsequently becomes available" that was likely to affect the outcome.
"And as a public body, our decision-making is of course subject to judicial review – which means our decisions come under scrutiny by the courts."
The ombudsman makes decisions on disputes between customers and financial firms that they cannot resolve themselves.
Last year it dealt with enquiries from more than two million people about bank accounts, credit cards, insurance, loans and pensions.
The Financial Conduct Authority has set a deadline of 29 August next year for the final PPI claims to be submitted.