Doesn't there need to be just cause? The DVLA will release the data to even a mere member of the public (for a fee) but only if they think you ahve a decent valid reason for needing it. So, if you are a private carpark bandit (note - not a proper car park person, they are clearly different, Robert!) then you can apply because you claim the car owner owes you money. But I'm not sure how far the justification goes - I'm not convinced that if I wanted to get hold of a car my dad owned back inthe '60s that DVLA would release the details.
As PXW says, if you have a valid reason then they will give you the info, they used to be a bit more flexible and you could get the details if you just wanted to offer to buy their number plate for example.