There are no no-fly zones on Hayling and, looking at https://notaminfo.com there are no NOTAMs for the coming week that would change that status.
Having said that there are the usual sensitive areas marked on Altitude Angel’s drone safety map when zoomed in. These are basically schools, cemeteries and the local nature reserve and the notes read:
" Yellow zones indicate regions where operation of your drone may raise security, privacy or safety concerns. This classification of area or point is likely to be additionally sensitive to privacy concerns. You may have greater obligations to disclose your intended flight over, within or near these areas to any controlling authority or land owner, particularly if you plan to fly with surveillance equipment."
Note that the satellite pictures were taken when the rape crop was ripe in the fields so that some of the yellow areas are not sensitive at all!
The indigenous Islanders have come to terms with the “small hard-shell bird him buzz like bee” and the bold few that may approach you are invariably friendly and will ask you intelligent questions like “was it you at Gatwick” and "don’t you need a licence for that thing?)