where it effectively means you can’t focus on a person as the main subject of the picture or video without their permission, but it’s OK if they are just in the background.

The law allows for that, however the implication of the literature released by the Home Office implies otherwise. They literally said "you can't photograph others without permission".

The main issue is that this is an official government publication, and as such people will regard it as factual. It's less that the law could come down on someone taking photos in public, but more that some self-righteous asshole might start a fight with someone taking photos, thinking the more strict version of the law the Home Office implied is accurate.

And there's also the slippery slope aspect of this being a potential first step to removing the right to photograph others without permission altogether.