Their frauds had affected 1.8 million people, the NFA estimated.
It said the stolen identities had been put to a variety of dishonest uses, such as buying goods or services, obtaining state benefits, or opening bank accounts under false identities.
The NFA, which was set up in 2008, said its figures had been worked out with the help of the National Fraud Intelligence Bureau.
Dr Bernard Herdan, the chief executive of the NFA, pointed out that stolen identities were often used to commit crimes other than fraud. This included dodging the police or other law enforcement agencies, terrorism and people trafficking.
"Stolen and false identities are a significant enabler of crime," said Dr Herdan.
"Losses from identity theft and false identities don't just affect the individual, but also hit the public and private sectors."
The NFA estimated that businesses and organizations lost £800m a year due to the expense of trying to combat identity fraud.
