Just like a car reg there is a driver reg called a driver number, they will have it if you where ever known to the DVLA.
It is a 16 character code made up using you name initials and date of birth. So Fred John Bloggs born 02/03/87 has a number where the first 13 digits are:
BLOGG802037FJ followed by NXX where N is numeric and XX is alphabetic (random)
If you Have a list of the addresses you have been at since you had a licence and work out the first 13 of your own driver number.
As others have said above they are a shower so they'll need som badgering but they probably do have you.
There are some variations if names are short and initials missing etc, here are the full rules:
http://www.crbs.org.uk/news/documents/Identity Checks.pdf