We are.
There seems to be a lot of info about why it can't be brought back into use, but nothing I can find about what destinations it served, or when/why it fell out of use.
For clarity, the island platform was originally numbered 1 and 2. They are now numbered 0 (the defunct platform) platform 2 renumbered Platform 1 and the western end of this platform has been extended to the original centre road and is designated Platform 2.
The trackbed for Platform 1 closed (from memory) in 1980. The actual trackbed is not on a brick arch, but iron girders. It was the suspect integrity of the cross beams that caused Platform 1 to be closed. You can walk under these today. The adjacent platform sits on the brick arch.
I live opposite Clapham Junction station for the past 71 years. The shuttle train running between Clapham Junction and Kensington Olympia for postal workers Since at least the 1950s was two trains in the early morning (0800 to 0900) and two in the afternoon (around 1600 to 1700). The service was nicknamed `The Kenny Belle` for reasons unknown.
It was steam hauled until mid-1967, and for many years not published. I used to travel on it as soon as I was 10 years old, just for the ride.
The train used platforms 1 or 17. Until 1967 the 4 carriages used for the service were stabled overnight in Pig Hill sidings adjacent to the West London Extension Railway just north of the tracks serving Platform 16 and 17.
The local passenger service to Kensington Olympia stopped in 21October 1940 owing to severe bomb damage, i.e. most of the wooden Battersea station burnt down.