This does not become a public highway, just because it does not have a set of gates. it is clearly stated that it is a private car park. It would be wise to erect a sign which clearly states that the area is a private car park and is for the use of staff and visitors only. That said, you must take as many steps as you possibly can to trace the owner with a view of having them remove it. If the owner is found and does not remove it, you can charge them for storage. (steps to trace the owner would be the Police & DVLA). If the Police trace the owner they may pay them a visit and ask them to remove it or they may inform you of the owner and let you deal with the matter. Should you be unsuccessful in this then I would suggest you place a note on the vehicle which states that if the vehicle is not removed within 14 days you/company will take steps to have it removed. After which time contact a local scrap yard and get them to take it away. The DVLA unit will not take it away for you cos it isnt on a public road/place