Victoria Station actually is historically two stations immediately next to each other. After the 1923 consolidation into Southern Railway, archways were cut in the walls between the two stations, forming one common station area between the street entrances and the platform gates. A common platform numbering system was adopted, with Platforms 1-8 on the Chatham side and Platforms 9-19 on the Brighton side. Outside the station, track connections between the two sets of tracks are minimal.
MAIN LINE: Victoria-Swanley-Chatham-Dover
4 tracks mostly Victoria-Swanley, 2 tracks beyond
From north to south, pairs of tracks identified as Fast, Slow (west of Brixton).
From north to south, pairs of tracks identified as Slow, Fast (east of Shortlands).
Between Brixton and Shortlands, Slow and Fast lines are separate, identified as Catford Loop, and Main Line (via Herne Hill).
Lewisham (from Nunhead)
Bat & Ball (Otford-Sevenoaks)
Sheerness Branch (1 track)
All lines 2 tracks unless noted. All lines DC electrification.
Number Of Platforms/Tracks: 8
Platforms numbered east to west
Platform 1-6 - Fast Line
Platform 7-8 - Slow Line
South of Victoria Station, the distinction between the Fast Line and the Slow Line ends south of the Grosvenor Bridge over the Thames River. And faster or slower trains might not necessarily assigned to these different lines.
Wikipedia link containing further station information and history.
Zoomable Google Maps along the various lines.