The Refuse Disposal (Amenity) Act 1978 places a duty upon local authorities to remove vehicles which have been abandoned 'in the open air':
http://www.legislation.gov.uk/ukpga/1978/3/section/3
That applies as much to private land as it does to public highways.
So it's your local authority which should be your first point of contact. They will need to establish that they vehicle really has been 'abandoned' (as defined by law), rather than just left there on a long-term (but still temporary) basis, before they can act. To do so they will place notices on the car and write to the registered owner to advise him/her that they will regard the vehicle as abandoned unless he/she contacts them, to show otherwise, within a specified period of time.
If it's found that the vehicle is not legally 'abandoned' then the land owner (or their agent) will have to take court action to get the vehicle's owner to remove it. (The threat of such action might be sufficient to get the job done). For such purpose the land owner/agent can apply to the DVLA for them to release details of the registered owner of the vehicle by using this form:
https://www.gov.uk/government/uploads/system/uploads/attachment_data/file/545606/v888-request-by-an-individual-for-information-about-a-vehicle.pdf