The DVLA will release your personal details on the understanding that the parking operator will not misuse them. The operator also signs an undertaking called the KADOE contract that they agree not to misuse them.
This paperwork "shield" against misuse is at best naive - at worst a cynical exploitation of the statutory obligation to give them your details.
If you think that your details have been asked for dishonestly or misused, you can write to:
Release of Information,
Fee Paying Enquiries Section,
Give your details and explain how you believe the information has been misused. DVLA will look into all claims where information has been requested inappropriately and will refer your enquiry to the Information Commissioner for prosecution if the need arises.
Alternatively you can send email the DVLA at firstname.lastname@example.org