Network Rail still have to go through a formal closure procedure if all passenger services are to be withdrawn from a stretch of line. It is easier just to keep a skeleton service going, which also allows drivers to maintain their route knowledge if the line is needed for emergency use (as it is this morning).
The Pasengers Services over unusual lines (PSUL) website http://www.psul4all.free-online.co.uk/2017.htm lists five weekday services over the Wimbledon-East Putney- Point Pleasant route
0042 Waterloo - Strawberry Hill
0105 Waterloo - Basingstoke
0454 Basingstoke - Waterloo
2254 Basingstoke - Waterloo
2312 Waterloo - Southampton Central
It was the 0454 which cane to grief this morning.
The route saw extensive use during the August shutdown.