You may be able to claim a prescriptive easement giving you the right to go over the car park land to access your garage - but only if you can demonstrate that this use has continued without serious interruption & without permission of the car park owner for at least 20 years.
However, it seems odd to me if a previous owner of your property built a garage with its access from the car park without getting permission from the car park owner to access it. If such permission was obtained it ought to have been recorded & included in your deeds & those of the car park. Have you checked your deeds - or the car park deeds? If not, get copies for a small fee from the land registry - make sure you go to the gov.uk site as a lot of other sites will sell you the deeds for a much larger sum.
Go here for more info. on prescriptive easements:
http://www.landregistry.gov.uk/professional/guides/practice-guide-52
As you can see, it is somewhat complex!