London Business School and National University of Singapore are highly competitive institutes and the acceptance rate is very low so you need to have a very good score in your undergraduate studies. Aparty fro stellar undergraduate you need very good score in GMAT. You need to have some very good LORs and you need to write a very good SOP. The SOP should justify your ambitions. You should have a fixed and motivated career path and you will need to justify it.

The London Business School does not publish an official acceptance rate, The acceptance rate is between ~10% - 20%, coming to the question, Well a high GMAT score is absolutely essential. Most school including LBS have a median score of 710. But if you have a score of 680+ and a strong profile, that gives you a fighting chance.Your academic background also matters, most schools want an ideal mix of engineers, economic, arts etc students so if you have a different background it helps, as it adds diversity to the whole school mix and scores good points on the international ranking scene. Here your nationality can also help, especially you are from one of those countries from which there are relatively lower number of foreign students studying abroad.

Your academics play a decent role, a high CGPA  shows that you are a consistent performer, but i know many people who have lower CGPA's but still score an admit. So it depends on how you explain your marks and whether you have a viable alibi for it. Also colleges know how hard it is to score top grades in certain UG colleges of the world, so they accordingly scale the marks and evaluate you. So no worries about that.

Extra curricular, well this is something i believe really, Well all these things have to be clearly explained to the school admission committee in your Resume and your Essays. Many people think that having a GMAT score is enough, but that's just the tip of the ice berg and is only one of the first screening techniques used by schools. An excellent, creative and well written essay or set of essays which showcase your multitude of talents is absolutely necessary!
Only by looking good on paper do you have a chance to be called for an interview and then actually explain all that you have already written about.
A Letter of Recommendation is also very important as it acts as a 3rd person certification of your exploits and gives the admission panel a view of your character from the eyes of somebody else. A lot of people don't give the LOR due attention and send half a page, poorly written LORs, this can be a strong cause for the demise of their application. So a well written LOR clearly explaining your strengths and describing experiences is absolutely essential and yes of course you have to ace the interview too ;)

So a well knitted culmination of all these lands you an admit into LBS and any other top school for that matter.

Hope this helps.