Chance me for UK schools - LSE + King's College (international student)

UK schools
I just received my LNAT score - I got a 33/42. The average for our cohort this year is 21/42. I’m still waiting to hear back from LSE and KCL. Is this LNAT score competitive? What would you say my chances are for these schools?

Other info -
SAT: 1560 (no superscore)
APs (taken): Five 5’s (US Gov & Politics, English Lang, US History, Seminar, Chinese), three 4’s (Research, Physics 1, Precalc)
APs (upcoming): English Lit, Euro History, Macroeconomics, Microeconomics, Stats, Calc AB, French
PS: I think my PS is pretty strong. I showed it to a lot of people with experience with UK schools and the feedback was overwhelmingly positive
Rec letter: Obviously no way to be sure but I am really close with the teacher who wrote it (my US Gov teacher) and he’s seen lots of law-related things I have done and knows me as a student and person. I also read some of the previous rec letters he wrote for summer programs and they were really awesome.

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