Driver identification numbers

Rather than the American driver licenses the British have driving licences. British drivers are each assigned a sixteen-character identification number that persists across license renewals. The last two characters of a driver number are check digits and Her Majesty's Government keeps the algorithm to itself.

With modern computing I can't help but wonder if the check digit algorithm would easily fall to basic cryptanalysis or even to a search through parameter spaces generalizing well-known checksum techniques. However, without access to a large set of correct driver numbers I am hardly in a position to look for any confirmation of my conjecture.