Hertfordshire itself does contain a large number of mines-dug for chalk, not sure if any are accessible... Significant workings in Hatfield and around Hemel Hempstead-recently been in the news owing to subsidence and stabilisation works. Probably the nearest accessible workings for you would be the Chislehurst 'Caves' (Mines), which is open to the public...just ignore *everything* the guides say about Romans, Druid sacrifices etc! ::)
BTW. At least couple of chalk mines dug in Bishops Stortford itself, although all entrances lost and built over
J
Over-ground, underground, wombling free...