England and Wales to fingerprint motorists at traffic stops

Via the Beeb:

Drivers who get stopped by the police could have their fingerprints taken at the roadside, under a new plan to help officers check people’s identities.
A hand-held device being tested by 10 forces in England and Wales is linked to a database of 6.5m prints.
Police say they will save time because people will no longer have to go to the station to prove their identity.
Officers promise prints will not be kept on file but concerns have been raised about civil liberties.
If the driver does not convince police he is giving them a correct name, they will fingerprint him and verify his identity on the spot, instead of taking him to the police station.

Assuming that 6.5m means 6,500,000, how is it that use of fingerprints can establish identity? The population of England and Wales is about 50,000,000. If 30% of this number are under the legal driving age (an overestimate, since 20% are 15 or younger), then 35,000,000 people are eligible to drive (I assume the number of those prohibited due to, for example, blindness or past offenses is not substantial). The Department for Transport says there are 31,000,000 registered vehicles in the U.K. Let’s be conservative and say that there are 20,000,000 licensed drivers in England and Wales.
If this is so, then a fingerprint obtained at random from a driver will match one the coppers have on file only a third of the time. How is it that this “verifies his identity on the spot”?
Rather than my back of the envelope stuff, I’d love to see some real numbers on the efficacy of this program. Unless there is a match in the database, how can this process do anything?