British Army nomenclature confuses an awful lot of people, especially Americans, and further especially because it has changed several times, sometimes leading to the same weapon having multiple names. Here follows a brief summary.
Really old-style, pre-1920s:
eg. Rifle, Magazine, Lee-Metford, Mk.II, abbreviated "MLM"
Rifle, Charger loading, Lee-Enfield Mk.I, abbreviated "CLLE"
Rifle, Short, Magazine, Lee-Enfield Mk.III, abbreviated "SMLE"
This latter was then re-dubbed, in the style from the 1920s to the 1950s:
Rifle, No.1 Mk.III
Revolver, No.2 Mk.I**
This system is significantly simpler than the preceding system which was terribly clumsy.
In the 1950s, the system was rationalised further:
Rifle, Self-Loading, L1A1
And so on. Watch out for the fact that many different categories of equipment share the same "L" number, as previously they shared the same "No."
Comparison with the American system
"No.x", "Lx", etc is equivalent to "M19xx" or "Mx", "Mk.x", "Ax" is equivalent to "Ax"
Hence, it makes about as much sense to talk about a "Mark 4 rifle" as it does to talk about an "A1 rifle" without giving any context.