Sancho :[and what isnt sustainable about the countryside.]
Very little of the countryside management is sustainable. Most of the work and produce is reliant on some form of petrochemical, or a substance derived from non sustainable sources, to give us the cheap food that we seem to demand.
Back to the OP; the idea is not viable as the NPs are designated as national, but, by and large, privately owned. What are you trying to achieve by charging? As a revenue stream is collected you would then have to plan the spending in the NPs. What are you going to spend it on? Do you want the parks turned in to theme parks? As areas that we as a nation have decided are of national importance are designated and protected by legislation. Taxes are collected and a portion of those taxes are used to regulate and control that park. That is where you can change the uses and protection of the parks, not by restricting access at the most basic level, by charging everybody to enter.