Welsh additions:
Kidwelly Industrial Museum - 1 - coal - preserved, not on original site. [note: moved from Morlais Colliery, Carmarthenshire]
Dolaucothi Gold Mine - 1 - lead - preserved, not on original site. [note: moved from Olwyn Goch Shaft, Milwr Tunnel Lead& Zinc Mine, Clwyd]
National Coal Museum, Big Pit - 1 - coal - not listed? in use.
Bersham Colliery Mining Museum - 1 - coal - listed grade II*.
City Shaft, Minera Lead Mine - 1 - lead/zinc - full size reconstruction of original wooden headgear.
Cefn Coed Colliery - 2 - coal - listed, grade II*. [note: not part of the adjacent Cefn Coed Colliery Museum]
Ffynnongroyw - 1 - coal - preserved, not on original site. [note: upper portion only; from Point of Ayr Colliery no.2 shaft]
And, as noted above: Parc - 1 - lead/zinc - underground, wooden. [I'd say there was sufficient remaining to count]
EDIT: Apologies - I see that in Part 1 you only want in-situ examples at working and closed mines, so some of the above, having being moved, won't meet that criteria (even if re-erected above shafts?). Or do you intend a part 2 list to include re-erected and replica headgears?