I thought the second photo looked familiar, and I found a higher resolution copy in my files. No idea where it came from however, but the time stamp on it was October 2016. I also a found a copy of the first picture too, same time stamp.
It's interesting that your copies are both newspaper clippings, while mine are scans of the original Photographs.
The site states that: “ By 1939 it was considered that a stronger box would be required during wartime conditions, and so the wooden boxes were replaced by brick structures with reinforced concrete roofs.
The question is, where were these police boxes located? I know of two sites: Sandridge Road (but that is a long road and a more precise location isn't yet known); and the junction of Beechwood Avenue (which had just been laid out) and Hatfield Road. ”
Now I don’t believe that a mere few years after investing in lots of wooden boxes the force would have demolished them all and replaced them with brick and concrete bunkers. Guess that new ones might have been made in this more ugly design. Interesting that the door might be the same as the wooden boxes and nice to have an indication of the colour too, at least in the 50s - 60s
The "Box" has moved a few yards North along the street to approximately where the Belisha Beacon is in your photo (looking in the opposite direction).
I wonder if it was the Market Beadles's Box
For example Borough Market has its own “police force”, the Beadles, who until the 1930s used to have powers of arrest and put offenders in the cells under the market.
The large building behind the box in your picture does indeed have cells in the basement!
The "Lamp" at thhe front on top looks more like a wooden finial.
Could be or possibly a police box having a second life as a market/ parking attendants hut like Sheffield. Which might explain the difference in colour.