Various designated areas have been created at various levels. Special Areas of Conservation (SAC), Special Protection Areas (SPA) and Ramsar (bird) sites are all European Designations under the Habitats Directive.
Local policies, such as local nature reserves, sites of nature conservation importance heritage conservation areas and strategic gaps, are set by the local District/Borough Councils, under national guidance. MSDC assessments are here.
Depending on what level the areas are will determine who administers them and how important they are seen in light of any planning applications.
Where designated, national parks authorities become the planning authority for the area. They will have separate policies for planning purposes, taking into the account the needs of the park. The new South Downs National Park will subsume the planning responsibilities of Mid Sussex District Council in that area.