Ed, you are correct that Birks Fell and Hell Hole (both the Stump Cross and the Whitewell one) still have a permit system in place, although permits are easily and quickly available by email. Your previous message seems to suggest they are not available by email. Have you had any issues getting a response to a permit request email for either of these sites?
Rest assured that with access issues now addressed in the core Three Peaks/Three Counties area, the CNCC is now looking to other areas. Birks Fell is a cave that the CNCC know needs to be brought out of the permit system as it is on access land and approached via a public footpath for the best part. There is absolutely no justification for any restrictions on caver access at Birks Fell. The matter has been discussed at a few recent meetings. However, the CNCC would prefer to engage with the landowner initially to achieve a harmonious solution. In the case of Birks Fell, the landowner is the National Trust, so communications may be challenging.
I am sure the CNCC Access Officer has given Birks Fell consideration and it will no doubt be discussed at upcoming meetings (which you are welcome to attend). At the moment however, resources are focused on addressing the rather pressing issues at High Birkwith, which are frustrating.
The CNCC have nonetheless demonstrated (during the recent Langcliffe Estate situation) that if they are not able to achieve a productive discussion with landowners, they will step back from unfair and unwarranted access agreements and will happily endorse open access under CRoW even if this goes against landowner wishes. The decision to do this would be carefully considered on a case-by-case basis.
The CNCC has been accused in the past of working more for landowners than for cavers, but this certainly isn't true today. Let's see what happens with Birks Fell.
My knowledge of the situation at Stump Cross is more limited; but the show cave owners have been extremely amenable over the years and have granted a lot of permissions for digging projects on their land and even in Stump Cross Caverns itself. Therefore, once again, achieving a compromise solution to eliminate permits is far more desirable that a more radical action (at least initially) to avoid complicating other accesses which are not covered by CRoW. I'm sure this is an area that will be looked at in due course.
The CNCC are aware people will visit caves without a booking or permit. Nobody is swooning in shock at such revelations. I don't think this is something they are concerned about about any more; the days of Access Officers getting called into Estate Offices for a telling-off are long gone, as are the myths of CNCC 'permit police'. The primary focus of the CNCC today is achieving maximum/open access with best possible landowner relations along the way. Naturally, the CNCC is going to encourage cavers to support whatever solution they come up with to achieve this.