When you add "the", you are referring to a specific English class. Thus, you already know what English class you are talking about. If you say "(An) English class starts at 9 a.m," you are referring to any English class, which, I don't think, is what you want to say.

If I were talking to someone who is in the same class, or is otherwise involved in the same English class, I would just say "English class starts at 9" or even "English starts at 9". It is absolutely correct to put the article before "English" but it mostly depends on context.

Perfect !

I would say 'The English lesson starts at 9 a.m.' But it depends if you mean some sort of class or lesson.