I'm no local but ridden a bit round Exmoor when camping there a few times and it's bloody marvellous round Minehead, Porlock, Wooton Courtenay, Webbers Post, Dunkery, Periton, Selworthy, Horner etc. Link all that stuff together and you'd hardly need to hit tarmac at all… More bridleways than you can shake a stick at, some nice technical stuff, rock gardens, eyeball bursting climbs and some fantastic downhills. Riding there with someone with local knowledge would be fantastic.
Only downside in the summer is the flies, of which there are many, and a large subset seem to want to be inside your mouth as you gasp for air on climbs. Presumably they go away in the winter at some point.