First of all, thank you very much for all your efforts.
Just now I was trying to find another unidentified button, possibly hunt, and to my surprise I found the button from this thread in Neil McShane's book "Hunt Buttons".
It is on page 287, "a selection of foreign hunt buttons" and it is listed as
Harrthiyah (Iraq).
This is very close to the "Harithy" brought up by Eddie.
So far I found that Al Harthiyah is an area of Bagdad:
http://wikimapia.org/5371386/Al-Harthiyah
Could it be one of many English hunts abroad?
To be continued ...