Most houses here have on the Deeds whose boundary is whose, and therefore whose fence is whose. But you can (I understand) put up your own fence inside a fence if you don't like your neighbours' choice. I always think it's good to be on excellent terms with the neighbours if at all possible. We are, on all 3 sides, they're all lovely and things are decided amicably. The only thing I absolutely hate is one chap who likes to put Creocote on his fence every 3 yrs or so. It makes me sick, dizzy and ill, and lasts for 3 or 4 days. But we still like them!
I think John's idea of windbreak small bushes is very good. They won't rot, won't blow down and look nice and natural.