Crikey, there are loads. The FODCA route is the most heavily used, and signposted, but there are miles of trails through the trees that the locals ride.
They are very subtle, usually only a slight opening through the trees along a fire road or tyre marks in some mud give a clue, and once in the trees the trails are barely marked, just branches laid on the ground and the larch needles being lighter where tyres flatten them and tyre marks looping around trees as the trail switchbacks and slaloms through the forest. Fantastic fun, if you are riding with someone who knows the trails intimately; I’ve spent an entire day riding in an area no more than a couple of miles from the cycle centre. Ask there if there’s a local rider or group you could meet up with who could guide you round. I used to ride with a mate who worked in John’s Bikes in Bath, who rides up there very often, and has done for many years, but I’m damned if I could find my way around on my own!