He & his mother were actually boarding at Rhossili when the 1911 census happened (apparently with other archaeologists, although she was originally from Glamorgan):
https://www.wikitree.com/wiki/Seccombe-122
A lot of the reports say the cave was excavated by Edward C. (Ned) between 1914 & 1919, but that could have been his father Edward Benjamin Howard (Ben) Cunnington, as Ned was in Egypt during 1916 & France 1917-18 (& died there - although he did have leave periods in between).
https://en.m.wikipedia.org/wiki/Ben_Cunnington_(archaeologist)