European struggle over Istanbul, Bosphorus Strait, Sea of Marmara and Dardanelles

A scenario: A European power manages to take control over Istanbul, the Bosphorus Strait, the Sea of Marmara and the Dardanelles some time before 1900. This was an important geopolitical goal for Russia, but maybe it would have been more likely that Britain would have taken control? Any views?
 
Bulgaria could have easily taken control of those areas if they wanted to. Or Greece, with those territories as the intended target of Megali Idea.
 
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