The High Court has delivered the final blow to a long-running legal battle over bank fees, upholding a decision that ANZ Bank was entitled to charge late payment fees of up to $35.

On Wednesday morning, the court dismissed with costs an appeal from ANZ Bank customers. Since 2010, they have been running a class action against the bank, claiming it unfairly overcharged tens of thousands of customers for paying their credit card bills late.

Lawyers for the customers had argued the bank's late payment fee of up to $35 was an unfair penalty, as the actual cost to the bank was a fraction of this sum.

A 2014 ruling from Justice Michelle Gordon found the fees were unfair penalties because they easily exceeded the 50¢ to $5.50 cost to the bank of a customer paying late.