Confidential data on two unencrypted CDs, including bank details, was lost by the UK government and has not yet been traced.
Customers are so alarmed that if the panic is not quelled, many banking clients may be in a rush to close their accounts.
Since the information that was lost relates to families claiming child benefit, accounts which are most vulnerable to identity theft are those which use children's names or dates of birth as passwords.
Millions of dollars are expected to be lost by the banking industry due to the event and high street banks have instructed staff on how to detect identity theft attempts and prepared them for an influx of customers attempting to close down their accounts.
A spokesman for Barclays said: "We've briefed staff to be extra vigilant on identification and verification with new account openings and changes of accounts. The extra checks are down to staff judgment, but we're asking customers to be patient."
If any fraudulent losses do occur to customers, banks are obliged to remunerate these under the terms of the Banking Code.