AHC : British Persia

During the 20th century, Britain occupied Persia twice during the world wars, and before that divided it up into two spheres of influence with the Russian Empire. It also had a station in Bushehr although that was moved to the UAE. Is it possible for Britain to formally colonize or declare a protectorate over part of or even all of Iran in the late 19th - early 20th century?
 
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