There's usually members of the Shropshire Caving Mining Club doing something on a Wednesday night. It could be Snailbeach, or possibly any other mine in the area (Huglith is another favourite) and they're usually happy to show someone around.
There are a lot of sites to visit in the South Shropshire area and around Oswestry (Llanymynych, Glyn Ceriog) and further afield are the Llangynog mines.