On Prop A (I had them labelled incorrectly before, only recently learned this so correcting myself now lol) there were these visible splits on the base, which is only on Prop A, with Prop B not seeming to have this same build marking, highlighted with the red circles
(Prop B top image, Prop A bottom- again had them labelled incorrectly last time
, always fun doing research and finding stuff out)
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It's a little more complicated than that! It's actually "prop A" in your top picture (I call it "A" for a reason that it was the box that was used
the most in
Season 1, while the other box only showed up a couple of times as a supporting prop).
Here is "prop A" in its original configuration, before the parts of the two boxes got mixed between each other:
And here's "prop B" in its original configuration as it appeared on Blue Peter in March 2005:
In your lower picture (from the shooting of
The Christmas Invasion) what you see is a "hybrid". Its both doors, front police box sign and the base are from "prop B", but its both front corner posts and the roof are taken from "prop A"! Except the roof has been turned 90° anticlockwise!
Just compare these two. "Prop A" on the left, "hybrid" on the right (with both front corner posts and the roof taken from "prop "A", but both doors, front police box sign and the base from "prop B"). I highlighted the very obvious dents which are the same between the two. Everything else (the base, front police box sign and both doors) is surely different, if you examine the woodgrain.
Here's how the roof turned out to be. "Prop A" on the left, "hybrid" on the right. Notice how "prop A"'s roof has been turned 90°.
And here's is another comparison. The "hybrid" prop on the left, original "prop B" on the right. Notice, that the front police box signs and both doors are the same:
