The lost discs contain personal information on 7.25 million families receiving child benefit, including dates of birth, addresses, bank accounts and national insurance numbers.
The quarter-page ads feature a hazard symbol and the headline: "Have your personal details fallen into the wrong hands?"
Although the government and bank officials are advising people to check their bank statements for "unusual activity", a spokesman for the monitor service said that this would not detect the long-term threat of identity fraud.
CreditExpert is an online credit monitoring and identity fraud protection service from Experian, the credit reference agency.
Consumers who pay £6.99 a month can monitor their credit rating online and will be notified by email or SMS if say a credit card company or a loan company has requested a credit check as part of a new application. The service will also monitor significant increases in credit card balances or whether a new account has been opened in a person's name.
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