I have now discovered some more information (extracts from the gun's handbook from which the above illustration came, plus more data in Campbell's 'Naval Weapons of World War 2') These prove my memory false, so I need to correct some of the things I posted above. What follows is my interpretation of the mix of information in my two sources.
There were two sub-calibre 2 pdr guns, designated High Angle and Low Angle. They were designed to fit within the barrel of 4" and 4.7" naval guns, and used the breech mechanism of the parent guns. At some point it was decided to make use of these for more warlike purposes, so they were fitted with a percussion breech mechanism and had a dual-purpose mounting designed, capable of taking either gun. That is what is shown in the picture above. So they were for active service, not training as I said.
In the Handbook, the Mk XI was stated to be used in Q.F. guns, the Mk XII in B.L. guns (which I find odd because Campbell lists all 4" and 4.7" guns used in WW2 as Q.F.). The Mk XI appears to use the short-case (40x107R) round as this is stated in the Handbook as weighing 2 lbs 10 3/16 oz while the Mk XII round is stated to weigh 2 lb 15 1/2 oz (and is presumably the standard 40x158R round). The muzzle velocities with a 2 lb shell are given as 1,900 fps for the LA gun (about right for the pre-WW2 40x158R ammo) and 1,100 fps for the HA gun (Campbell says c.1,200 fps for the Mk XI and 2,040 fps for the Mk XII).
Campbell states that the Mk XI had a 25-calibre barrel, while the Mk XII had a 40-calibre, which also supports the conclusion that they had different case lengths. Therefore, it is safe to conclude that the Mk XI used the HA gun and the Mk XII the LA gun. He also states that 180 Mk XI guns and 170 Mk XII were produced and fitted to HDMLs (Harbour Defence Motor Launches) and other small auxiliaries, and that case shot was also provided as well more conventional ammo, at least for the HA. The implication is that both HA and LA cartridges used the same projectiles.
To put all that together, it seems that the Mk XI was the HA gun firing 40x107R ammo and in its sub-calibre training form was probably originally intended to work with 4" and 4.7" HA (anti-aircraft) guns, while the Mk XII was the LA gun firing 40x158R originally for sub-calibre use with surface-fire weapons.
I hope that it's now a bit clearer. :tinysmile_eyebrow_t