There is almost zero focus on grammar in the UK. It is assumed you pick it up naturally. They teach you how to use punctuation correctly, apostrophes, full stops, semi colons etc. but the actual nuts and bolts of the language itself is not really taught. And it's not really necessary I suppose, you assimilate the grammar naturally just by being surrounded by the language day in day out. I remember being taught a noun was a 'thing', an adjective was a 'describing word' and verbs are 'doing words.' And 'adverbs' are 'adjectives for verbs (cringe)'. That was about as in-depth as it got. I've seen people from the US comment before on how they were taught the 'parts of speech' but if I ever learned that school I certainly don't remember it! That is why people who have not studied a foreign language or linguistics will often not have a clue what learners are referring to when they mention things like 'phrasal verbs', 'participles', 'pronouns' and the such like. English classes concern themselves more with how to write different kinds of things, as Jmat described above. As you move into secondary school you start to focus more on literature, how to analyse things and how to write in a cogent fashion using the skills you developed previously.

Well, English speakers don't actually learn English grammar at school, we pick it up as toddlers. English classes in school are mostly focused on writing things like essays, newspaper articles, editorials, book/film reviews, letters, film/play scripts, short stories etc. We generally have to memorise a template, and then practise structuring whatever we're writing according to that template. As for literature, I think just about everyone studies Shakespeare's plays at school e.g. Julius Caesar, Macbeth, Hamlet etc.