LONDON—During the swinging ‘60s, Epping Forest, on London’s northeastern fringe, gained notoriety as a favorite haunt of the city’s mobsters. These days, criminal activity in the forest has less to do with who’s being buried in its glades than what’s being dug up: Epping Forest has become London’s epicenter of wild-mushroom rustling.

Soggy, gray England is a paradise for fungi, which thrive in damp, shady areas. Foraging bits for supper has become a foodie craze. And for the commercially minded, mushrooms have a high resale...