I seem to remember there are a lot of paths in England that cross private property but are accessable to the public.

There are. But rather than just being gentlemen's agreements that can be changed on a whim (which happens in the US a lot), they have various laws that designate footpaths that are ALWAYS open to the public plus the "right to roam" off those paths as long as you are not causing damage or interfering with livestock, game and/or farming.

The US is all about "it is my land, no trespassing" while over there it is pretty much the exact opposite.

I'd be worried that the next owners may not like hikers on their property.