Hi A
British Colonial Badges, and British Colonial Badges II, both by Renfrew, Renfrew, and Cranston. ISBNs: 978-0-9563175-1-3 and 978-0-9563175-2-0, cover many badges from Arab nations formerly British colonies/protectorates/mandates.
The Military and Police Forces of the Gulf States: Volume 1: Trucial States and United Arab Emirates, 1951–1980 (Middle East at War Book 16) by Cliff Lord and Athol Yates. ISBN: 978-1-912390-61-8, covers the Trucial States/UAE military and police insignia in depth (although it lacks information on uniform buttons
) is well worth getting. I think there is a sister volume on Bahrain and Qatar(?) in the pipeline.
Hope this helps
Graham