Cambridge University Library has an online catalogue of the SPR's archive.
CUL has looked after the SPR's main archive (minus the audio-visual element) since 1989. They have produced a catalogue covering the period 1749-1998 which gives an outline of what they hold on our behalf. This is a work in progress and there is still uncatalogued pre-1998 material, plus post-1998 acquisitions.
https://archivesearch.lib.cam.ac.uk/repositories/2/resources/13400
The SPR's archives are still growing, and we welcome donations of suitable items.