I remember reading an article regarding this some time ago as well. It's mostly due to some new rule that when the public has been able to access private land for an amount of time unhindered the state can claim it their own. This has caused most to fence up in order to keep their land.
It's completely understandable, and this is mostly just Government trolling to land owners and causing inconvenient situations to the public wanting to access public grounds.
Because there's no perfect solution. If a piece of land has that much utility the government could take ownership (possible compensate the owner) and be responsible for maintaining and upkeep.
I mean your example in the UK, I can't believe every landowner that has a public right of way on their property is thrilled about it, especially in cases when they went to do something with their property and the government told them no because of the right of way. What good is owning that property one might wonder? If it's that important to everyone why not have the government purchase it and maintain it?
Every landowner might have a different opinion of what the best solution is. Good luck writing a law that appeases them all.
Here the local authority is responsible for upkeep (though in practice they may not have the budget). Landowner responsibility is pretty much just don't block it or put anything dangerous there.
It's completely understandable, and this is mostly just Government trolling to land owners and causing inconvenient situations to the public wanting to access public grounds.