You're right, Sorcha (as usual) -- I did some searches and came up with only a "British Light Infantry" in the DT. Lotsa threads re Ulster, but I didn't check every one that looked promising; I have to go away soon for a bit.
So, johntm, tell us more about these songs: where did you hear them, who was singing, what's the gist of each song, do you remember any snatches of the lyrics...? Every little lead helps. 'Catters thrive on this, but all hints are considered clues of great import...
Alas, commitments call. Will check back and try to search more later. ('Course, by then, the Mudcat Honor will doubtless have been upheld by others, and all your queries answered. Ah, well; we part-timers do what we can.)