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[Edited by bluenote86 on Apr 11, 2022]

Hi, I would say you got a chance. I base this solely on my own research into the profile books of BCL/MJur students. 

If you would like to see how you compare you can have a look at student profiles here (you can find other years with a google search):
https://www.law.ox.ac.uk/sites/files/oxlaw/faculty_of_law_-_bcl_profile._final_copy._tst.pdf

Naturally this will only give an indication of what the department is looking for. If I were you I would consider it worthwhile to try. Parts of your paper would also likely serve as a good sample for the written work you need to submit with your application.