Eleven million Nationwide customers may have been put at risk of identity crime after an employee's laptop was stolen.
Nationwide said there has been no loss from customers' accounts
The computer with customer information on it was stolen during a domestic burglary three months ago.
But details of the serious security lapse are only just emerging.
Nationwide has informed the authorities and will be writing to its 11m customers to give them security advice in the next few weeks.
It is reassuring customers that no PIN numbers, account passwords or memorable information was on the laptop.
But it does not deny that names and account numbers could have been.
If this information was obtained by identity thieves, they could attempt to take out credit cards or open loans in customers' names.
So far there is no indication that has happened according to Nationwide and it said nobody has lost any money.
But if the data is used by criminals it could be some time before any evidence is seen and the fraud attempts may not involve Nationwide.
The names and addresses could be used to attempt fraud elsewhere.
Diane Gaston of the National Consumer Council told BBC Radio 4's Money Box she is angry customers were not told sooner.
"A three month delay is appalling. People should be able to trust that if a problem has happened they will be told about it straight away."
Nationwide is still refusing to give much detail.
It said it is following police advice and does not want to cause alarm.
It said the laptop was "security protected" but would not explain if that meant the data was encrypted or coded to foil identity thieves.
Peter Wood from computer security firm First Base Technologies told BBC Radio 4's Money Box he did not think it would be difficult for thieves to access the data.
Chat rooms are full of people trading credit card details online in real time at all hours of the day and night
Peter Wood, IT security expert
And he warned: "The chat rooms many people use are full of people trading credit card details online in real time at all hours of the day and night."
The financial regulator, the FSA, and the Office of the Information Commissioner have both been informed.
They say they are continuing to discuss the situation with Nationwide.
But neither is taking any other action at this stage.
BBC Radio 4's Money Box will be broadcast on Saturday 18 November at 1204 GMT.