The section of Belgrave (http://www.aditnow.co.uk/documents/Belgrave-Lead-Mine/Belgrave-Mine-Survey.pdf) shows it as extending quite a distance (presumably along the lode) across Bryn Alyn, so probably both locations are applicable.
CPAT mines index (http://www.cpat.org.uk/projects/longer/mines/18005.htm) has a description of the surface features and references Foster-Smith, J R,
The Non-Ferrous Mines of Denbighshire (British Mining 5), 1972.
http://www.coflein.gov.uk/en/site/33922/images/BELGRAVE+MINE/ All the above sources (and other references I've come across) refer to Belgrave Mine rather than Bell Grave, so I would suggest that the photos currently associated with Bell Grave be moved and the entry for Bell Grave Mine be deleted.
Dave