Writing in the latest issue of Ombudsman News newsletter, Ms Ceeney commented on the NatWest computer systems problems which left thousands of consumers unable to access their accounts.
She said: "The recent situation involving people's day-to-day banking seems to have been unprecedented in scale. It affected more people immediately - and it could send ripples that might be felt in some surprising places.
"I am confident that if the banking sector acts now - and shows a genuine commitment to re-building trust and supporting affected customers - we shouldn't see many complaints later on."

The FOS currently receives 1,000 new cases each day and received 57,590 between April to June, over half of which related to payment protection insurance.
Trust in the financial services is a significant issue and as a result Financial Planner Shane Mullins launched his Question of Trust campaign yesterday. The campaign aims to increase trust in the industry and is supported by the Institute of Financial Planning.
Mr Mullins said: "All it takes for mistrust to thrive is for good men and women to do nothing. Today we have the opportunity to make our presence felt.
"We need a humble response and root-cause action right across the industry, coupled with strength of leadership and a commitment to take the long-view to change things for the better."