I give tuition to students in their homes. So I am a "home tutor". I teach English to students in their homes. So I am an "English teacher". How would you express this in a single phrase? Home English tutor
or English home tutor
I am a 'home tutor of English' works best.
I am an 'English home tutor' could be interpreted as being from England,
but can be used.
Since 'home tutor' is the profession, those two words stay together.