The construction had started. A gap between the houses near Edgware station was built for the future tube line to go along. The construction of this viaduct had also started. Behind the viaduct was the planned location for Brokley Hill station. Land was also cleared to make room for the tube line to reach the planned stations of Elstree South and Bushey Heath.
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However, WWII broke out and the plans were put on halt. When the war ended, the plans were abandoned.
What's left today:
The gap for the planned tube line near Edgware station has been used for housing now and can still be clearly seen from the sky. The houses built in the gap are also more modern and narrow than the surrounding houses. Dead end roads were also placed next to the gap and are also still there today. Next to the A41 lies this (thumbnail) unfinished bridge abutment and behind it are the remains of the unfinished arches for the viaduct at Brokley Hill station. The rest of the line after Brokley Hill never started constructed and no traces can be seen.
At Edgware station you can also see behind the buffer stops the built, but never used tunnel that would have been part of the extended Nothern line. On the other side of the station you can see where the line would have come over ground again, but that tunnel portal has been buried.
An interesting video explaning the whole thing in more detail:
https://www.youtube.com/watch?v=jjuD288JlCs