According to Major Gordon, a quick though not 100% accurate source on things Asian, there were 11 infantry, 6 cavalry, and 6 RAF squadrons, plus Gunners and various support units, who qualified for the IRAQ bar. Many of those will have been on the NWF in 1919, plus the transferred officer mentioned above and those Indian units who did qualify for a Victory Medal.
Apparently the rolls are available on the open shelves at the National Archives but that's more info. than you'd need. Naval Military Press will happily sell you a copy of Gordon's 7th edition, the most complete and correct one for that era and area, but it doesn't appear to be available on line.