It was a fiasco! They fingerprinted it but they also drove it around, used it as a prop in the reconstruction etc.
If you search for B396 GAN at
GOV.UK - Enter the registration number of the vehicle, you find it was taxed until 1 August 1990, four years later. I don't know how accurate those results are from so long ago, but if that is correct, then the car was presumably still being driven around on the roads for another four years, otherwise why would you tax it?
Astonishing way to treat the only surefire crime scene. I would guess they still have it.