Some customers of the Yorkshire and Clydesdale banks who were charged too little on their mortgages, have fended off demands to pay arrears.
The customers took their complaints to the Financial Ombudsman Service (FOS), which has upheld some of them.
The Yorkshire bank said only a "very small number" of customers had complained successfully.
Borrowers were told in July they had been undercharged because of a mistake in calculating their monthly payments.
Both the Yorkshire and the Clydesdale are owned by the National Australia Bank.
For the previous two years the banks had incorrectly recalculated the capital repayments the affected customers were expected to make, as interest rates dropped.
"The vast majority have accepted it was a genuine mistake and their payments are changing to reflect that," said a spokesman for the Yorkshire bank.
Some of the customers who contacted the BBC in July said the banks should accept their mistakes and write-off their arrears.
They argued that they were now being asked to repay several hundreds pounds more per month, for the remaining terms of their loans, to pay off arrears running into several thousands of pounds.
The Yorkshire bank argued that these were extreme cases.
"In the majority it was a very small change to their mortgage repayments - half of those with a shortfall are paying less than £25 a month extra," said the spokesman.
He explained that of this figure, between £2 and £3 was due to the past underpayment, and the rest had been put in place to bring the monthly repayments up to their correct level.
The FOS publishes figures every six months about the number of complaints it has received concerning each financial institution.
These are broken down under general headings such as banking, mortgages and insurance.
The FOS refused to disclose how many complaints it had received about mortgage underfunding specifically, for either the Yorkshire or the Clydesdale, or what the result of the complaints had been.
However the Ombudsman has recently explained that where a lender is entirely at fault it will usually rule that the arrears should be cancelled.
The Yorkshire bank acknowledged that some customers had been successful.
"Some borrowers complained to us and some have gone to the Ombudsman," said its spokesman.
"It has found in their favour in some instances and we are going along with that.
"There are instances where the ombudsman has found in favour of the decision we have made," he added.