From 1854 until 1900 trains ran every day, but eventually traffic started to tail off as road transport became more common. Originally the trains left from Waterloo but in 1902 they moved to a purpose-build station on Westminster Bridge Road. However, in 1941 the station was bombed by the Nazis and, due to the decline in passengers, it was never reopened after the war.
You can still find the station at 121 Westminster Bridge Road, just to the south of Waterloo Station. For more information, see http://en.wikipedia.org/wiki/London_Necropolis_railway_station.