My grandson told that all the grammar he really knows well, he has learned through his Latin lessons. Thus, àfter primary school.
You grandson learned the bulk of his grammar at home when he learned how to speak. The problem is that the grammar of one's spoken (first) language is definitely different from one's written formal language. It is not clear that learning some formal grammar (i.e., the terms for parts of speech and some grammatical functions) improves one's grammar. It does give you a way to talk about grammar. It's seems for most people who complain that grammar is no longer taught in schools grammar is a random bunch of usage, orthographic, and punctuation rules (masquerading as grammar), learning to identify parts of speech, and maybe some diagramming of some sort (either the Kellogg-Reed diagrams, or TG trees).
The best thing you can do, either as a kid or a grownup, is to read and write a lot. Taking a second language (like Latin) helps, too. Finally some elementary linguistics, such as pointing out that there are different registers that one uses to accommodate the social part of communication.
I think those things can be taught between the reading and composition parts of a normal English (or Dutch) curriculum.
