Do native English speakers use a word 'study group'?
Opinion: The term "study group" is often used by native English speakers and given the alternatives that you've suggested I would say that "English study group" would be my preference over all of these. If your intent is to simply indicate participation in a particular time when the study group met I would go with "English class" (formally lead by an instructor) or "English study group session" (informally directed by the members of the study group)...