@clacke There are definitely newspaper style guides. To the extent that your needs overlap with a newspaper's, The Guardian's guide is perfectly fine (on their website). Hart's Rules is also fine, very book orientated, and is good at pointing out the elements of style about which one needs to take a decision.
Generally, I find questions of style strangely fraught in English. There's the question of the many dialects, but also a systemic pedantry that aspires to the loathsome Académie française. So many style sections of dictionaries and style guides, will give rules that are not followed by the great writers in the language. Rather than cite T. S. Eliot and Virginia Wolf and William Faulkner and James Baldwin and so on, they'll make "rules" that none of those writers followed.
The OED is mostly a decent counter-example, relying heavily on citations of known good works. But then, to answer your comment
I don't know quite where the Greeks come in
If you look up the question of ise vs ize endings in the OED, you'll be treated to a pedantic discussion involving classical Greek, the letters iota zeta eta, Latinisation, Middle French, etc. So they go contrary to conventional British usage and make a weird pedantic argument. The peculiar style they advocate exists and is relatively common in certain circles, but is a bit of an elite aberration.