It's traditional that any cross struts, or downward batons face into the garden of the owner of the fence but I don't think it's a legally enforceable requirement. Our back garden fence, owned by our neighbour, is just being replaced and as he is doing the work himself putting up a closely boarded fence, he has asked if we would mind having all the rails our side as this would make it easier for him to erect and avoid him having to come into our garden and trample down all our plants in the process.. We were happy to agree.