I hear that there may be an official agreement between cyclists and whoever owns / manages the land for access there by bikes.
The agreement used to be that any riding in Leigh Woods was OK, as long as it stuck to established trails, no building of new ones, and no riding in sensitive areas (SSSI and a few areas that were heavily used by walkers).
The new trails aren’t explicitly a replacement for the old unofficial stuff, but they do mostly follow the route of the best-known unofficial trail. The MTB trails cross loads of walking tracks but the new trail is designed in such a way that you have to slow down at potential conflict points. It also avoids most of the “desire lines” down the sides of the Avon Gorge, which are pretty much all SSSI.
Just out of interest, are you just planning to come here for a ride or is there a similar proposal for your local spot? If it’s the latter, email me and I can put you in touch with some of the people behind the Bristol project.