An extract from the 1952 (1:1250 Scale) OS Map showing the Tower and grounds --
I've prepared a section of this OS map showing the relevant corner of the Tower with an overlay of where the 1939 City of London Survey of Kiosks and Posts places this "Police Cabin." There are some scale and orientation issues near the edges of that Survey map (particularly with the south end of the Bridges), and CoL 1 was on the right edge so shows some distortions, but below shows the range of positions depending on how one deals with these --
The green circle of each position is the extent covered by the number marker for CoL 01 on the Survey Map, with the red dot being the centre, where more often than not I've found the actual 1939 locations for the surveyed Posts and Boxes to be. The upper left set are those when biasing the overlay to the corner of the Tower grounds and the Tower Bridge Approach, while the lower right set are those when biasing the overlay for the average of the more accurately drawn western and northern parts of the Tower and all the surrounding buildings and streets. The darker green is the area common to both (vesica piscis), a useful averaging of the margin of error here.
The results are not perfect, but fairly close nonetheless. If the positioning is as with most of the rest on the Survey, the most likely area is within a smaller circle barely encompassing the two red "centre" dots. So it would appear that the CoL "Police Cabin", whatever it was, is marked as having been in the vicinity of the Salt Tower (upper right red marker is more or less centred on same), with the highest probability that it was between the inner and outer walls.
The aerial photos don't seem to show anything at that location, but it's very hard to get a good angle because of the proximity of the walls and buildings. It should also be noted that there are open arches within both walls so it's always possible it was in one of these, essentially nestled under/within the wall.
I've been unable to find any ground photos in the appropriate time periods, but these show the area in question:
East side of the Salt Tower looking north between the wall curtains - probably around 1900-1910 --
South side of the Salt Tower looking east between the wall curtains - c1910 --
A relatively current view of the area at the base of the Salt Tower within the curtain of the inner wall --
Perhaps someone could take a field trip to the the Tower at some point and ask some pertinent questions of the Warders or staff?