I think you might be confused. There is no MPhil in philosophy at Oxford; the BPhil is just the philosophy equivalent of what is called the MPhil in other subjects. (As a historical side note: when Oxford first introduced two-year taught master’s degrees in the late 1940s, they were originally all called BPhils. But this tended to confuse outsiders for obvious reasons (a master’s degree called a bachelor’s), so in the late 70s the University decided to change the name to MPhil — except for philosophy, which was allowed to keep the BPhil title because it was the oldest and best-known of the programmes with a great deal of existing name recognition in the English-speaking world.)
The only other master’s programmes that the philosophy faculty offers are the one-year MSts in ancient philosophy and the philosophy of physics. But given what you mentioned about your background, I assume these would not be relevant to you.
Regarding your second question: the faculty is explicit that the BPhil is *not* intended as a conversion course in philosophy. The vast majority of those admitted have done at least joint-honours philosophy degrees at undergrad. Very occasionally I think they will admit candidates who haven’t done so; these typically tend to be people with first degrees in, for instance, politics or law with a very strong background in political or legal philosophy. So not having a first degree in philosophy is not automatically disqualifying, but I suspect it will make life very difficult for you in what is already a very competitive admissions process.
As far as sociology in particular goes, I suspect many of the theorists you look at will be somewhat alien to what is still the predominantly analytic focus of the BPhil (though it is certainly more pluralistic than it once was). If you can give me more detail on what exactly the philosophically relevant content you’ve studied in your undergrad is, and what the areas of philosophy you’re interested in are (in particular, what topic you’d consider doing your writing sample on, which is the most important factor for admissions), then perhaps I can give you some more specific advice on how realistic a candidate for the BPhil you’d be.