http://www.c**tplaces.co.uk/phpBB2/viewtopic.php?t=3414&highlight=willimsons+tunnels
Willimsons Tunnels under Liverpool can provide a good underground experience, not sure on the access but dare say it is in the link. For natural your closest is North wales, but Derbys and Yorks generally has more to go at and easier access. For artificial again N Wales - it is riddled with mines, and the slate around Ffestiniog has some huge underground workings. For someone to go with try the lifts and partners board, or try clubs in the area... do you have your own transport?