A distressing DVLA (NSL limited) related issue

Okell

Have you complained to DVLA, NSL or both?

I would suggest you should be complaining to DVLA that their agent, NSL, (1) wrongly removed your vehicle and (2) damaged it, but won't admit liability.

You might end up having to sue DVLA and/or NSL through money claim online if neither coughs up.

Assuming NSL did cause damage to your car when removing it, it's that damage that you need to be claiming from DVLA and/or NSL.

I doubt you can claim for feeling unsafe or violated or persecuted.  Those are not reasonably foreseeable responses on your part.  You can tell all your neighbours that the car was wrongly towed - which is the truth.