Thanks again, Mark and Sandra,
I think the Tollgate in the Seaside area sounds the more likely - as there seems to be such uncertainty about this Seaside area of Eastbourne prior to the 20th Century, and even after WW1, perhaps I need to pay a visit to Eastbourne again and have a browse in the library there; or take myself off to Lewes Record Office to look at maps.
This Spring, sometime...
Best wishes,
Keith