The stations and extension were planned and construction did start. However, WWII broke out and the plans were stopped and since then have been abandoned.
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What's today:
As WWII broke out before the construction of Elstree South, nothing was ever built. The planned location of the station has now been occupied by an Esso petrol station.
An interesting video explaning the whole thing in more detail:
https://www.youtube.com/watch?v=jjuD288JlCs