Does English possess a term for the study of all aspects of language in primary/secondary schools

There's no 'official' term on this side of the Atlantic, perhaps because education is less centralized in the US than in Europe.

In the upper reaches of the educational ladder there's a long tradition of awarding honorary doctorates in "Humane Letters" (Litterarum humanarum doctor: DHL or LHD), but I don't find anywhere a Faculty or Department of Humane Letters.

In primary and secondary schools the term Language Arts is gaining currency, though it appears to be used more of instruction at levels below high school. Language Arts, a publication of the National Council of Teachers of English, describes itself as "a professional journal for elementary and middle school teachers and teacher educators."