I'm not sure about berkshires but I dont think you would have a cat in hells chance of keeping tamworths in for long behind a tape! There well known for being vey good at escaping!
In terms of what is in the woodland I wouldnt worry about most thing but I definatley would not put the Pigs any where near the yew tree. I'm not sure if the y berries are toxic, the stems,leafs and roots contain high levels of toxins which when ingested will attack all of any animals internal organs leaving them coated in a thick tar - resulting in a very quick sudden death, and there is no treatment once eaten!