Durham will not be an issue for law unless you want to go into a top commercial barrister set, and even then the competition for that is so extreme that even Oxbridge candidates’ chances aren’t great. Having said that I believe my director of studies went there and he now works at a very respectable commercial set.
My understanding is that Durham is not a solid “target” IB university (I’ve heard it described as a “semi-target”) which might possibly prove problematic if you’re applying for really heavy hitting roles, but the extent to which it’ll hinder you is not something I know enough about to comment on.
Another thing I wanted to say is that (and this especially applies for Oxbridge), that personal statements are usually fairly minor components of the admissions process, with academic performance, admissions test scores and interview scores being far more important. If you got rejected from Oxford then I don’t think it was just the personal statement that was to blame. With that in mind, coming in with a stronger personal statement the second time around is unlikely to substantially improve your chances.
You might have a better shot at LSE, though.