Correcting various points:
The council planning department is nothing whatsoever to do with land ownership held by the council - the people who would know will be within a legal section of the council - typically part of the finance section of it. But if one is intending to occupy land, one doesn't go about asking who owns it. If one is complaining about somewhere else's actions one has go about finding the rightful owner (if there is one).
Tree-chopping may be frowned upon but trees are only protected if they have a TPO on them or if the area is within a 'special area' - Conservation Area, AONB etc. Most areas aren't.
It would be a civil matter to chop a tree on area one doesn't own, but unless a land-owner knows/shows up, nothing will happen.
Land has been 'purloined' and claimed in this manner for 100s of years, with occupation for a period of time being the main criterion for the occupier to establish a legal right - historically often involving a court case. Since a land registration system was established in the 1920s, the opportunity to register one's interest in the land has been possible (but not compulsory until relatively recently). The Limitation Act of 1980 established the oft-quoted 12 years of occupation as being required before Adverse Possession claim is possible. But that only applies to unregistered land.
Eddie's final sentence tells a lot - the worst that can happen is he / you are asked to move the cars. I should get in and share some of the action but it is useful to you also.