The taxpayer will have to pay £270m to customers who have personal loans with Northern Rock Asset Management, which has been in public ownership since the financial crisis.
152,000 Northern Rock customers will receive an average of £1,770 each because bank staff failed to include key details on annual statements, including the original amount which had been borrowed.
The problem arose with personal loans of less than £25,000, many of which were provided on top of Northern Rock's Together mortgage which was popular before the credit crunch and allowed homebuyers to borrow more than their homes were worth.
The failing arose as a result of an investigation by UK Asset Resolution, which looks after rescued banks for the government.
The Treasury said that it had commissioned an investigation from the consultancy firm, Deloittes, which would report early in the New Year.
It adds that UK Asset Resolution has the financial resources to cover the payments to customers.
How the £270m will impact on the public finances will be decided by the ONS, but it is likely to increase Public Sector Net Borrowing in 2012/13.