You don't need a reason, just ask for all information they have stored on you. They are entitled to charge upto £10 to cover administration costs.
2. Release of information about yourself - Driver Register
Enquiries of the Driver Licence Record should be addressed to DCS (Data Subject Enquiries), D4, DVLA, Swansea SA6 7JL. You should give details of your address, driver number or full name and date of birth and reason for request. A fee of £5 is payable.