1. What you describe certainly seems to be an error on the land registry - they should not have the same property registered under two different title numbers.
2. If the land in question is registered at all, you should be able to find out who owns it by making an enquiry based on a plan showing the area of land you are concerned about. If necessary, talk to the land registry about how to go about this. You should also give them the 2 title numbers you so far have & point out the error - it just may be that one of these titles is supposed to be for the land & they have got them mixed up somehow.
3. If you will not own the land and the use by the present house owner has only been for 4 years then you will not acquire any inalienable right to go on using it for parking so - assuming the parking is essential for you - it is vital you get some proper written confirmation of the position (giving you a permanent easement and not just a licence) from whoever does own the land.
You will have to decide whether this is all too much hassle for you. If it is then you will no doubt decide to pull out. (Incidentally, was a HIP done? If so, it should have included documents to clarify all this!)