Banks and building societies are warning customers to be alert after HM Revenue and Customs lost discs holding personal details of 25 million people.
Two discs containing the details of 25 million people have been lost
Customers are advised to monitor their accounts closely and notify their bank of any unusual transactions or other suspicious activity.
There is no evidence that the compromised data has led to any fraud.
Under the banking code, customers would be reimbursed for any losses if fraud did occur.
Most banks have already reported an increase in inquiries and online traffic.
A spokesperson for RBS said it had seen a spike in calls, and warned there was a chance that some customers might not be able to get through immediately.
But the bank cited the advice given by both HMRC and the chancellor that there was no need for people to contact their bank unless they had specific concerns.
Staff have been briefed to direct concerned customers to HMRC's dedicated helpline, but beyond that, the message is one of reassurance.
HMRC CHILD BENEFIT HELPLINE
"The risk to customers is extremely low," said a Nationwide spokesman.
The discs lost by HMRC contained sort code and bank account details, National Insurance numbers, dates of birth, and names and address details of all families in receipt of child benefit.
But banks insist the information would not be enough to let criminals access customers' accounts.
"It is a serious breach," said a spokesman for Lloyds TSB, "but fraudsters would need lots of other personal information to be able to get through all the other security layers that are in place."
"From our perspective, there's nothing to suggest there's been any increase in suspicious activity," he added.
WHAT CAN YOU DO?
Check your bank statements for odd transactions
Monitor your account if you bank online
Change your account password if it is a date of birth or name
Check your file with the three credit reference agencies
Banks are also reminding customers to follow the "normal safeguards" regarding personal data. These involve shredding receipts and statements, keeping Pin numbers secure and never sharing passwords or other security information.
"Our advice is that customers should be vigilant," said HBOS's Mark Hemingway.
"The bottom line is you are protected under the banking code in the unlikely event that any fraud is carried out, but there are things you can do to protect yourself."
"Monitor your account carefully, and if you have a password which involves a date or birth, or any of the other information which may have been lost, then change it," he added.
Any unexpected account activity should be reported immediately.
Barclays has said it has reviewed its internal security procedures as a result of the data breach.
"We have briefed staff to be extra vigilant, and will be asking customers for additional information as well," a spokesman said.
"Obviously we won't say what those extra measures are, but we are asking people to bear with us, as we take all steps to minimise the risk to customers."
All the banks, and the industry body Apacs, are stressing there is no evidence that the mislaid data has led to suspicious activity on any customers' accounts. But the position is being watched very closely.
"Across the industry we have a robust and comprehensive monitoring system," said a Lloyds TSB spokesman.
"A range of additional measures in terms of surveillance has been put in place," he added.
Customers who are concerned about the risk of ID fraud can check their credit file with the UK's three credit reference agencies, Experian, Equifax and Call Credit.
They can also take out "protective registration" via the fraud prevention service CIFAS. This ensures further identity checks must be made before credit is granted.