Some of the fungi can be toxic. There are deer on Exmoor and Oct is the rutting season, so they may get a bit frisky with you. Just dont try to get too close.
The most dangerous quadraped is probably sheep. On a descent of Cheddar Gorge, they kept jumping out from the side. Even top racing cyclists have been felled by sheep, they are totally unpredictable.
2nd most dangerous QP is horse. There are lots of riders on quiet country lanes. You can always tell a regular horse route from their calling card. If you do see horse dropping, assume they come from a horse that is around the next blind bend. On narrow lanes between hedges it is easy to spook a horse.
ps I recomend Cheddar Gorge, from E to W.
In the East (Kent/Sussex) there are (feral) wild boar: escapees from farms. I havent heard of any problems, and they are less aggressive than the truely wild continental variety.