Hi,
I did my MSc at LSE as well, so maybe I could be helpful. I don't know that there is any minimum threshold, and i think it's much more about you overall (ie work ex, publications, statement of purpose etc) than just being confined to GRE and your grades at LSE. that said, i would think that if you're aiming for top 25 then you should probably be aiming at 65+ to make a strong case for yourself. i don't think a low merit would have that kind of a cache, just because about 80% of the MSc students at LSE get a merit anyway, so the higher up in the 60s you can manage, the better (ie upper 60s - since distinctions are notoriously difficult. i remember in my department only one out of about 75 got a distinction).
however, a MSc grade of 60+ would probably be countered for by great and relevant work ex (or a very strong dissertation grade, especially if your area of interest at the PhD level is very linked to your dissertation topic).
hope this helps!