In the same issues of Cave & Karst Science, there was an update on the caves and karst in the Chalk of the Eastbourne_Brighton area.
https://bcra.org.uk/pub/candks/index.html?j=143. I suspect that there are new several entrances at the western end of Beachy Head Cave where the original survey shows it comes pretty close to the cliff.
FARRANT, Andrew R; Louise MAURICE, Eleanor MATHEWSON, Matthew ASCOTT, Graham EARL, Debbie WILKINSON and Steve HOWE. (2021). Caves and karst of the Chalk in East Sussex, UK: implications for groundwater management. Cave and Karst Science 48(2), pp65-83.