Is there still a public right of way through "their" land up to flinty fell quarry?
As Ben says the tracks are open access, but the game keeper does not like vehicles past the compressor house and will give you hassle unless he gets to know you. You can get access to drive up to SC / CH if you ask NPHT, best is to ring in advance.
I would recommend caution when it comes to gamekeepers up there. Even if you can't see them the chances are they are watching you. Its easy to wind them up and the knock on effect is very detrimental too mine exploring. After a couple of instances a few years ago of people removing shaft covers to have a look and then not bothering to cover them up again the gamekeeper doesn't look favourably upon our kind on occasion.
Also bear in mind things that effect him like nesting times and shooting days. When wandering up there we are having fun, they are trying to make a living.
As regards the fee charged by the Heritage Centre my personal preference is to tell them where to stick it.