I lived in the UK for three years as a kid. We visited the Lake District, for example. I had no idea it was mostly private land, just assumed it was all a National Park.

I'd be skeptical of depending on private ownership of lands to maintain access to nature.

Are European countries acquiring lands to create parks or trail systems? In my local community, we have a private non-profit that works to acquire lands to maintain greenbelts. The priority is habitat, but the properties are usually open with trails, (no camping). In 1967 Oregon ensured a permanent public easement for access and recreation along the ocean shore seaward of the existing line of vegetation, regardless of ownership. The bill was modeled after a Texas law, apparently. This should be the norm...