[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):
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.