The NFA estimates 1.8 million people have their identities stolen each year, but most are not aware that they have been targetted.
Stolen identities are used to carry out credit card and benefit fraud as well as other crimes, including evading the police and terrorist activities.
The NFA, which released the figures to mark National Fraud Identity Prevention Week, said the issue demands a co-ordinated response by the government and the private sector.
Just over 79 000 people were victims of fraud in the past year, up 10% on the same period the year before, according to UK fraud prevention service, CIFAS.
CIFAS said people should check accounts and financial statements against receipts, and before responding to calls or e-mails.
Only about half of UK residents carry out such checks, according to the latest CIFAS report.
This story was first published by Computer Weekly