I.C.1. Another possibility
It would appear there may be another explanation for that "I" marked on the receivers of the earliest Martini-Henry carbines.
According to page 127 of Temple and Skennerton's, "A Treatise on the British Military Martini, The Martini-Henry 1869-1900", under the heading of, THE FIRST SERVICE PATTERN...
"This was a direct development of the sixth trials pattern carbine, and was approved for service on 24-9-1877 as the "Arms, Interchangeable, Carbine, Breech-loading, Rifled, with Cleaning rod, Martini-Henry, Mark I". It will be noted that it was not described as a CC, as at this stage it was intended that the artillery should also use it, in conjunction with a side arm - swords for garrison artillery, sabres for horse and field artillery."
This leads me to think that perhaps, I.C.1., actually stands for Interchangeable Carbine, Mark 1, and not, 1st class Carbine, Mk 1, (a marking style not used on any other British arm before or since, that I can find), nor, Infantry Carbine Mk.1, (another marking style I can find nowhere in any of my references.)
Realizing there are probably plenty of reference materials I don't have access to, I would be most happy to learn from what source these other theories are taken, but until then, I will trust Ian and Barry, as Interchangeable Carbine, Mark 1, seems to make a bit more sense.
Merry Christmas and Happy Hannukah to one and all!
All the best,