I understand the CNCC have made approaches to Mike Cooper about making the contents publicly available, but he still hopes to publish a new edition at some point so isn't keen on that idea. I think the unwillingness to print a new run as-is is because some of the information is out of date. It will take a lot of work to update it though, so that is likely to be some way off.
In the meantime, this is what caving club libraries are for! Most (all?) Dales club libraries have a copy of the Black Book. As a club librarian I will happily copy and laminate relevant individual pages for club members for the purposes of taking on trips underground, and I'm sure other clubs have similar arrangements. Presumably that's acceptable practice
@David Rose, if the copies are disposed of or kept in the library for future use?