The Royal Bank of Scotland (RBS) and its NatWest subsidiary have been fined £2.8m for poor handling of customer complaints.
The Financial Services Authority (FSA) imposed the fine, finding there was an "unacceptably high risk" that the customers had been treated unfairly.
Failings identified included poor and slow dealing with complaints.
RBS accepted its performance on complaints handling had been poor.
The company said: "We recognise the importance of complaint handling for our customers and are focused on addressing the root causes of complaints."