I'm not British, but I should think it's the context that defines how the word is used. Just as "***" is a specific term for an animal, as well as a rather rude term for the buttocks, "bloody" can mean blood-soaked, or it can be used as an oath.
According to the Online Etymology Dictionary, it has been "a British intens. swear word since at least 1676." That source goes on to report "that it was "respectable" before c.1750, and it was used by Fielding and Swift, but heavily tabooed c.1750-c.1920, perhaps from imagined association with menstruation; Johnson calls it "very vulgar..."
Eric Partridge, in Words, Words, Words (Methuen, 1933), suggests six possible origins, prompting the idea that blood is simply vivid or distressing as the most probable. He also downplays the suggestion that it originates from "by our Lady" (an invocation of the Virgin Mary) as being phonetically unlikely (to whit I agree).
I've also heard it said that it comes from an old oath, "God's blood," (i.e., the blood that was shed by Jesus when He died upon the cross). The Oxford Dictionary of English Etymology says this is "probably" the origin, but the OED says "there is no ground for the notion".
In short, we may never know for certain of the origin.