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?
 
I can't see that happening after ww1 unless the Persians nationalize the oil. Persia is just too big too populous and the terrain to rugged.
 
Maybe if the ruskies get up to some shinnanigans during the great game or if the Persians nationalize the oil fields. It can't really be proper colonization though, It would be more economical for the british to just install a '' puppet shah. Any more than that and I can see this as Britain's vietnam
 
Perhaps with a bigger Russian threat to Persia the British would intervene more directly and turn Persia into loose protectorate
 
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