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Do the BCL if you are even the slightest bit unsure about that PhD. EUI is great but 3 years is a long, long time to spend on one topic and everyone I know who has done or is doing a PhD has impressed on me how CRUCIAL it is you are passionate about your topic. I can't stress this enough. You can always do the PhD later when you have had time to think further on the topic.

If you are serious about academia, do the BCL. Then apply to some Phd which involves teaching and is a paid position. A lot of universities in Europe give you that opportunity. Oxford for academicians is unsubstitutable except with Yale or Harvard.

I would also say it really depends on where you are from and what legal academia is like in your home country. In the United States, LLMs are not really considered at all in academic hiring (with a few limited exceptions, such as LLMs in tax for people wanting to focus on tax law). Getting a second LLM, regardless of where it was from, would do pretty much nothing on its own to help an American academic get a position. I say "on its own" because if you use the year to do a fair amount of research/writing, then you can rely on any articles coming out of it when looking for academic jobs. But the degree itself doesn't help in the hiring process.

Unfortunately, because the BCL is course-based instead of research-based, it doesn't really give you time to write that thesis-based programs would, so I would not recommend it for a second LLM if you wanted to break into American (or Canadian, for that matter) academia. Instead, I would recommend something thesis-based, like the M.St. program at Oxford, the M.Litt. at Cambridge, or one of the thesis-heavy LLM programs in North America.

Of course, things may be entirely different in Europe, South America, Asia, etc. But I would honestly be surprised if academic hiring committees the world round did not expect you to do substantial research and writing at some point.

(Before anyone claims sour grapes on my part for not getting into Oxford, I am talking about *second* LLMs - my plan if I went to Oxford was to do the M.Phil. after the BCL.)