The main audience for Orwell in writing "Shooting an Elephant" was the English people as a whole.
The point of the essay was to argue that colonialism was a bad system -- that it hurt both the colonized and the colonizers. He argues that the colonizers lose their integrity and their moral values when they rule over others.
Since he's arguing against colonialism, it makes sense for him to direct his argument at the people who could actually do something to either improve or end colonialism
The people who could do that were the English public.