As Remoteneeded says, really not much in that part of the world, in Bucks itself you're looking at the odd chalk mine, but all small-scale stuff, few larger mines in parts of Herts (around Ware, Hertford, Chadwell) but still nothing amazing. Ditto Norfolk, Essex
Was interesting stuff in Northamptonshire, but all now sealed, so you're looking at either Wilts as mentioned, Derbyshire, or the Godstone/Merstham mines in Surrey and the haunts of the Wealden Cave and Mine Soc...
West Wycombe aka Hellfire Caves are interesting, nice way of spending maybe couple of hours (though take everything you hear/are told with a large pinch of salt!)...or there's always the Chislehurst Caves (MINES)...whole truckload of salt needed for the 'history' told here! :lol:
J
Over-ground, underground, wombling free...