Once our rights are gone they will be gone forever.
In essence there are only two types of land, land is either publicly owned, or privately owned.
Given that none of us ever had the right to park up and stay the night on privately owned land without the land owner's consent, I guess you're referring to publicly owned land such as lay byes and other such places.
If you park in a lay bye or other public land and act responsibly I fail to see how you would fall under this legislation, i.e. you wouldn't cause or be likely to cause significant damage, disruption or distress, therefore the Police would have no power to require you to leave.
My local pub has a large paddock at the rear which is used by the caravan club. Last summer about 20 cars and caravans pulled up, uninvited and not members of the CC, they made themselves at home, refused to leave and were intimidating toward the landlord and his family. Pub takings dived as people didn't want to park near these wasters. Police simply told the landlord that they had no power to require them to leave as it was private property, he would have to go to court for an order. A week later they moved on, leaving a mess behind as expected.
That's a situation replicated up and down the UK and the legislation is long overdue, IMO.
Of course, we don't have to see things the same and I hope your fears about the implementation turn out to be unfounded.
It is worth remembering that a Police Officer can stop any car driving on a road, at any time and any place, without grounds to suspect you of anything, and ask your name, address etc. (Road Traffic Act 1968)
That's a very significant power - how often, in your experience, do they exercise that power?