Belgrave mine is open and there are two adit entrances (one above another) and they are on a footpath (well, just left of a footpath) halfway up a hill around SJ 197 593. There is a small road you travel along just north (100ft?) but lower in altitude to the entrances and you should see the footpath stile around those co-ords. Go over the stile and walk up the hill and veer off the path after around 100-150ft to the left and you will see the lower opening (it's quite small). The higher opening is above it (directly up the hill) about another 100 ft. (both entrances are crawl in but you can stand up and walk as soon as you are in). Both levels have shafts down to lower levels but you will need up and down gear if you want to venture down.
Bog mine is at SJ 205 572. It is a depression in a field (there is a capped shaft between the road where you park and the bog mine entrance which is a giveaway that you have arrived). the entrance is just on the otherside of the fence past the shaft. The entrance hatch is locked and the key is "with" UCET caving club but is located nearby to the hatch (PM me if you go and I will tell you precisely where it is).
The capped shaft is corroded on one side and can be entered with ab gear (we have not done this) although there is a stream running into it (which caused the corrosion) and I do not know the depth of the shaft. When you are in Bog mine you cannot find this shaft so we assume it is a different part of the mine even though it is within 100 yards of the entrance. You should be ok with just cows tails as there are ladders and knotted ropes where needed which were ok on our last trip.
UCET caving club can give you more information if you need it .....
Also, there are pictures and videos from both of those mines on the webby (perhaps that's where you saw them?)
www.ucet.org.uk
Hope that helps
Ian