James.
If you have proof that you had sold before the alleged offence took place (as you state you have), then why are you worrying?
As others have said already, the people who work there have, in my experience, no ability to communicate between departments (like all of the civil service and 95% of companies in general!) and no interest in "doing the job right", so basically you have to do things that they should do.
Next time you call do the following:
When you finally speak to a human, get their FULL name and the department they work in before you even say anything more.
When you get transferred (entire Government departments are created for this purpose!) do the same again.
Explain in a calm and determined manner the whole situation and that you have absolute proof that the car was sold by you prior to the alleged offence.
If they state it will be sorted, say thank you and you want that in writing in the next 7 days (they work in geological time so you have to expect this).
If they say "sorry, computer says no" then calmly tell then that you now wish to resolve this matter in front of a magistrate and tell them that as part of this process you are requesting copies of ALL documentation held by them about this matter under the freedom of information act. You will need to follow this up in writing, ask them for the FULL address (ie actual department).
They are legally obligated to provide you with this information (although they could charge a small administration fee).
Let us know what they say after that.