It must be on their boundary, not encroaching on your land - and usually planning permission is required for a fence over 6 ft high. They certainly can't leave it so that it has hazards (i.e. nail points) on your side. Have you pointed these things out to your neighbour? Who did you speak to at the council, the planning officer? Is your home and theirs privately owned, or rented (in which case you could involve the landlord)?