An error after a software update has caused thousands of Clydesdale Bank and Yorkshire Bank customers to make incorrect payments on their variable-rate mortgages.

In a statement, the banks have admitted to miscalculating around 18,000 borrowers’ repayments, which has led to customers underpaying. It said that the calculation has now been corrected, but affected customers may face increased monthly repayments as the banks try to recoup the money customers should have been paying in line with their mortgage terms.

A spokesperson for the bank declined to name the software involved, adding that the problem was with adjustments the bank made to its systems. "We made changes to our systems to allow for greater flexibility [of payments] for customers. This created the inaccuracy in the calculation."

The software was designed to calculate the minimum amount borrowers needed to pay, which varied according to the base rate. The bank said that the inaccuracies were made worse by the Bank of England making several rate cuts over over a short period of time during the recession, which did not allow the calculations to make the correct adjustments in time.

“It created several underpayments one after the other,” the spokesperson said.

The banks said that it has “suggested” new regular payment amounts in letters to individual, affected customers, explaining that it reflects the correct monthly amount plus an amount to correct the shortfall caused by the underpayments. It has already written to 99 per cent of the affected customers, but said another 180 customers will receive their letters in the next couple of weeks.

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“For around half of the customers who have been underpaying, the total suggested increase is less than £25 a month, of which around £2 is to cover the shortfall,” Yorkshire and Clydesdale banks insisted.

However, according to The Herald website, some customers are seeing their monthly payments rise by up to £300. The site also reported that many customers who have been offered compensation of up to £500 by the banks, have refused the offer.

Steve Reid, retail director for Clydesdale and Yorkshire Banks, said: “We are very sorry that this error has happened and for any inconvenience it may have caused those customers affected.”

The banks said that they have now corrected the calculation "so that it is industry standard" and had it reviewed with third parties to ensure that it is "accurate going forward".