Their island status presumably stopped them being affected by s.27 of the Poor Law Amendment Act 1868, under which the remaining extra-parochial areas either had to become civil parishes (as Calke and Derby Hills did), or be joined to the parish with which they shared the longest common boundary.
I just noticed that the OS also stopped marking Lundy Island as a separate civil parish in the 1950s. Would that have been big enough to avoid falling into the same administrative black hole?
Or perhaps the OS decided they shouldn't have been showing Puffin Island as a separate civil parish, since it was really extra-parochial (according to the census reports up to 1971). A similar change seems to have happened with Cardigan Island and Caldy Island at the same time, for example.
