That which is not required is forbidden (strictly forbidden)!
I thought I might pass on some of the rules about using National Parks in my neck of the woods here in the United States.
First of all, you can't do just anything you want, contrary to what some may suggest, just like in the U.K. Unfortunately, the situation appears to be getting worse but not necessarily in the way you might think I mean. But first let me explain some differences.
There are national forests and there are national parks. The national forests are theoretically intended for multi-purpose uses and generally are. There are limits on camping but generally the attitude is a lot different from national parks. You can have campfires and you are not required to camp "out of sight." I don't know about the permit situation, however, but you cannot camp just anywhere. There are a few shooting ranges in the George Washington National Forest but I've not been to one. Otherwise, regarding firearms, all other laws apply, especially game laws. Also contrary to what others may suggest, there is no reason to have a firearm anyway.
The national parks and here I am mainly referring to ones like Shenandoah, east of Washington, D.C., are supposedly recreation oriented, though they sometimes go to some length to make that difficult. You can camp in the backcountry with a free permit but there are no cleared places that are really good and safe to put up a tent. So, you pretty much have to camp under the trees, which makes me nervous on a windy day. All in all, the camping regulations suggest that people really ought to stay out of the park. With that comment out of the way, there are generally good lodges in national parks that are a great way to spend a weekend, especially if you don't care for sleeping on the ground (under the trees). You also can't have a fire except in very limited places and you can't stay more than two nights in one place.
The National Park Service seems to be going through the mill right now. I believe there are fewer rangers around and trail maintenance, except for the Applachian Trail, is not what it used to be. The reason for fewer rangers is, I suspect, a more important requirement for rangers elsewhere. Then, the fees have gone up. It costs $10 for entrance by car and an annual pass is $30, which really isn't so bad, provided you make it up there often enough. It even costs extra to use a certain number of especially popular trail. Otherwise, you can walk in for free just about anywhere and the camping permit is still free. These comments probably apply to any similar park although there are all sorts of other parks within the NPS system, like National Seashores.
Sometimes you hear stories about illegal activities going on, like growing illegal plants (imagine, making a plant illegal!), though drunkeness is likely to be a more realistic problem at large campgrounds. Otherwise I doubt anything dangerous or harmful goes on in the backcountry, which is not to say everything is always strictly legit. Oh, yes, the parks have designated wilderness areas but I refuse to admit that they are in fact, wilderness.