The company said fraudsters could wait until children turn 18 before trying to apply for credit in their name.
Compliance director Helen Lord said this could have a "catastrophic effect" on their ability to buy or rent a home or obtain a loan or credit card.
The Association for Payment Clearing Services said vigilance was vital.
Jemma Smith, from the association, said: "The information is no doubt valuable in a thief's hands."
Children aged 15 to 17 whose names, addresses and dates of birth were among the lost data are at risk from determined fraudsters prepared to wait for lengthy periods before using the data, Experian said.
"The fraudsters will wait until they turn 18 and start applying for loans, credit cards, mobile phone contracts and other credit products in their names," Ms Lord suggested.
"That could have a catastrophic effect on their ability to get on the housing ladder, rent a flat, obtain their first credit card, obtain a loan for their first car, even open a bank account."
Experian said warnings from banks and the government to check statements carefully were not enough to prevent people falling victim to identity theft.
Instead, the agency said people should monitor their credit reports to ensure no unauthorised checks were being carried out, something which would indicate someone was applying for credit in their name.
The BBC's Jane Peel said anyone concerned could apply for "protective registration". This places a warning against their address so if anyone applies for credit in their name, it will be double-checked.
She said one official at a High Street bank had told her: "This will be on the radar for decades."Chancellor Alistair Darling has stressed that so far there is no evidence that the missing data has fallen into criminal hands.