i actually know of people who got accepted into Oxbridge but not LSE for LLB. i also have never heard of any NUS folk being rejected by LSE LLM...it's always a guaranteed for NUS because NUS is well recognised.

heard that for the US LLMs they have much lower acceptance rates for Singaporeans. for example, columbia LLM takes in maybe at most 5 Singaporeans (and mostly need work experience), penn LLM takes in 1 or 2 Singaporeans.

in any case, LLM is not useful for practice, and as long as the school sounds reputable and you take some relevant LLM courses, i'm sure it would suffice lah.