It is really hard to see in these photos. It appears to me that the badge on the sun helmet and the shoulder title are two letters. The last letter is an "H", the first letter maybe an an "L" or an "I". I've tried matching what I can make out of the cap badge with the titles and no luck. Thought I may have had it with Irish Horse, but there were two regiments a North and a South. Badges, however, don't appear to match up.
The UK did purchase Ross rifles early in the war, but do not know who they were issued to.
I just noticed there are at least two troopers with slouch hats in the photo. Some of the Yeoman Regiments did have these as well as the ANZAC units.