I did a quick breakdown of "The List" to show totals for specific installation dates as there is some reason to suppose that many, or even most of the closely associated installation date groups were implemented as part of individual projects, probably involving tenders from multiple companies for their completion (see "The Rise and Fall of the Police Box" as reference), with the contract usually going to the lowest bidder. This would go a long way towards explaining the many different versions of Boxes we see in the photographic record (I count at very least 4 distinct box patterns (most visible in the roof and sign box configurations) in addition to the wood/concrete-roofed originals and the very different "Mark 3's", though this is a quite cursory observation and likely there were more).
If we can pin down the location of boxes in the photo record (with approximate dates) and associate them to specific installation groups, it may be possible to eventually form a more clear picture of which "Type" or pattern of box was erected in a particular group or contract, perhaps eventually also associating them with a specific builder. We may also get a better idea if any particular type was used as a replacement for damaged or destroyed boxes (Mark 3?).
Regrettably, "The List" doesn't appear to give a record of any changes to a given box (or its replacement history), only the commission and decommission dates for the site itself along with some occasional all too brief comments.
Regardless, hopefully this will be of some use:
02 Dec 1929 --
22 Boxes in V Division (known to be original wooden models w/ concrete roofs - built by Messrs. Grove and Sons - some evidence only the pierced metal "POLICE" signs were installed initially)
20 Jan 1930 --
20 Boxes in Y Division (known to be original wooden models w/ concrete roofs - built by Messrs. Grove and Sons - some evidence that explanatory placard below the phone cupboard and St. John badge in opposite panel were part of the standard installation by this time)
13 Oct 1930 --
16 Boxes in V Division (type not known for certain, but presumed to be the first all-concrete versions from a new contractor - Somerville and Co. Ltd. - if so, "globe" style red beacon still being used (though possibly with new mounting hardware), with hopper windows and backlit glass "POLICE" signs (blue letters on white) now standard)
16 Mar 1931 --
20 Boxes in V Division (continuation of the V Division experimental installation project, probably with the same contractor)
20 Apr 1931 --
11 Boxes in V Division (completion of the V Division Project and presumed to have been built by the same initial concrete version contractor - Somerville and Co. Ltd. - noting that what pictures I've seen of the early concrete boxes show them to be of a pattern quite distinct from either Barnet or Crich as evidenced by differences in the sign boxes, pillars and roof)
30 Nov 1931 --
22 Boxes in W Division (possibility for a new contractor with a new pattern of box for new project/tender, but unknown if actually the case)
18 Jul 1932 --
18 Boxes in W Division
02 Jan 1933 --
17 Boxes in Z Division
03 Apr 1933 (5 not fully dated, but likely same)--
32 Boxes in Z Division
01 Apr 1934 --
13 Boxes in Y Division
02 Jul 1934 --
30 Boxes in P Division
13 Aug 1934 --
17 Boxes in P Division
08 Oct 1934 --
43 Boxes in K Division
05 Nov 1934 --
37 Boxes in R Division
3 Posts in R Division
(Anomaly - PA1 Pillars were by some reports never used by the Met and yet the Met Posts were not designed until 1937)
08 Apr 1935 --
7 Boxes in Y Division
22 Apr 1935 --
19 Boxes in Y Division
06 Jan 1936 (though 3 not fully dated likely the same -- known from photographs to be a new pattern of Box more like Barnet) --
53 Boxes in J Division
13 Jan 1936 --
69 Boxes in S Division (All Barnet type Boxes? Barnet is among these (S63), but it is unknown if all in this group, and/or in adjacent groups, were of the same Barnet Pattern (and thus presumably built by the same contractor). Signage is still of the 'Mark 1" pattern, save that by this time the top signs read "POLICE PUBLIC CALL BOX" (though still in blue letters on a white background and now in a serif typeface) and the top beacons are of the familiar Fresnel configuration (though possibly still red in colour). It remains unclear exactly when these changes were implemented, but they appear to be firmly established by this point.)
04 May 1936 --
66 Boxes in X Division
20 Jul 1936 --
68 Boxes in T Division
18 Jan 1937 --
2 Boxes in W Division
09 Aug 1937 --
13 Boxes in L Division (possibly the first installation of boxes with the classic "Mark 2" sign configuration as original fitting - applies to whole group)
13 Boxes in N Division
4 Posts in N Division (probably the first of the classic rectangular pattern Metropolitan Pillar installations (PA2))
4 Boxes in W Division
03 Jan 1938 --
7 Boxes in B Division
9 Posts in B Division
15 Boxes in F Division
1 Post in F Division
7 Boxes in G Division
3 Posts in G Division
11 Boxes in H Division
8 Posts in H Division
9 Boxes in M Division
8 Posts in M Division
24 Jan 1938 --
1 Box in A Division
4 Posts in A Division
1 Box in C Division
7 Posts in C Division
3 Boxes in D Division
10 Posts in D Division
1 Box in E Division
9 Posts in E Division
29 Jan 1938 --
1 Post in A Division
The rest seem to be low volume additions or replacements to the system (Crich and/or Mark 3 boxes and PA3 posts?):
Jan-Feb 1948 --
2 Boxes in P and W Divisions
15 Jul 1948 --
1 Box in W Division
Nov-Dec 1948 --
4 Boxes in Z and V Divisions
Jan-Feb 1949 --
7 Boxes about a week apart in P and W Divisions
Dec 1953 --
1 Box in S Division
1954 --
2 Boxes in T Division (The 2 Heathrow Airport Mark 3s)
21 Oct 1958 --
1 Box in S Division
1959 --
1 Box in M Division (Last entry for a Box)
1 Post in M Division
1962 --
2 Posts in R Division
1963 --
1 Post in C Division
1 Post in F Division
2 Posts in H Division
1 Post in M Division
1 Post in R Division
04 Aug 1965 --
1 Post in A Division
EDIT: Corrections to above figure made based on proofing of transcribed Met List/Database by comparing to original scans. Original Met List transcription as posted and linked in this topic has not been altered, but Metbox Database has been corrected.