I have just added this to the map of places to fly your drone at Drone Scene:
Land owner permission requirements unknown.
Though not shown as such on the map Pagham Lagoon and Harbour is designated as a nature reserve and is an internationally important wetland site for wildlife. It is 629 hectares (1,550 acres) in size. The Reserve is made up of saltmarsh and tidal mudflats with shingle, open water, reed swamp and wet permanent grassland habitats.
Pagham Harbour’s 600 hectares are home to some impressive historical heritage, including medieval forts and the old Selsey Tram embankment. Part of the site is protected as a Scheduled Ancient Monument (SAM).
Its habitats and wildlife are also protected as a Site of Scientific Special Interest (SSSI), a Local Nature Reserve (LNR), a Special Protection Area (SPA), a Marine Conservation Zone (MCZ) and a RAMSAR Site.
It is suggested that you fly with caution, especially times when birds may be nesting or disturbed by drone activity.