Curiouser and curioser. I'd gleaned my original information from the Historic England documents and that sent me towards New Downs Farm & Princes Golf Course. Although I'd looked at various threads on here, including the one with the hotel, I'd missed that composite with the mast. That would seem to knock Historic England's theory out - and mine, too.
I took a better picture today, though whether I can do better than provide a link remains to be seen.
Apparently not. What am I doing wrong?
Many thanks, everyone. All input is really appreciated.
ETA: I've also made the error of using the 6" and not 25" maps, until now. That's inexcusable and had I done so before pointed that way, I might have looked at the coastguard station more closely. The 'North Tower' and 'South Tower', for example. My photographs yield nothing on any of the maps prior to 1938 so I think I must be wrong.