The UK is a small, densely populated country without large areas of true wilderness. Over 90% of the country's land is private. The one area of the UK where there are large expanses of land without many inhabitants is Scotland (due to the Clearances), but the land there is still mostly owned by large land barons, and so Scotland has a more permissive law that allows non-destructive access to almost all private land (Land Reform (Scotland) Act 2003).
The US is almost half public land, it's absolutely gigantic, and it has numerous areas where you can be hundreds of miles away from the closest real settlement. We don't need traditional paths and easements and whatever when we have millions of acres of National Forest and BLM land that you can access freely. There are land barons in the US, but by absolute area, they did a fairly poor job of buying up the country's land before the federal government could protect it.