It's often not the content but the tone and way it comes across.
Aye, the BBFC take context into account for the content.
So two scenes with basically the same content could be rated quite differently depending on the context of those scenes.
The BBFC have become much more open and communicative about how they work over the years, and in the last couple of years have been doing podcasts talking about how they came to decisions, both in general and concentrating on specific genres or individual films.
I've only listened to a few of them but they're actually interesting as they discuss things like the circumstances and history of the decision (say it's a cast covering a film that was made and certified 30 years ago, and recertified*), what they legally have to take into account and reactions to the decisions.
You can also read a brief reasoning behind decisions made in the last few years on their webstie when you search for the film from memory.
*I think they did an episode on Mad Max, which over the years went from an 18 with cuts, to a 15 uncut.