interesting question - I fired straight over to the Hitch and Hike site - as they used to maintain a fairly comprehensive list of caves access details - here http://w01-0504.web.dircon.net/pdc/caveguides.htm
but its been bagged of in favour of their PDF mini guides (which are great by the way) .
So then to the DCA site where all I could find was this by following the Access Information link on the left hand side.
http://www.thedca.org.uk/Circulars/2000-3.htm#holme
"Holme Bank Chert Mine
Ownership of the building block firm, Smiths Runners Ltd, has changed hands and the new man-in-charge, Mr Oldfield, wants indemnifying. He is prepared to allow access to continue as before whilst DCA sorts out indemnity provision. However, the telephone numbers given in the Handbook are to be discontinued and the new number to ring is 01629 813301, between 8.30 am and 5.30 pm. All visiting groups are advised to have valid PL insurance cover. "
Now - its from 2003 - so may not be current.
This raises an interesting question about access (sic) to access agreements - which I'll spark up in a new thread.