I went to NLCS in the late 70's to mid 80's. It may be very different now, but agree that then there was a mix of backgrounds, both culturally and financially, and it wasn't a 'snobby' school in the way of say Eton or Roedean. It was more 'elitist' in that it aimed to create highly educated, academic women, who could achieve the same or better than men (there was a definite 'feminist' slant at that time). There was certainly little or no emphasis on appearance, manners or similar.
If I lived in London and could afford it (neither apply to me!), I would still not send my daughter there for various reasons:
a)Teaching my daughter that she can achieve anything she wants in life is not realistic. When I went there, this was the attitude and there was never any discussion of having children and how to juggle that into your life. This may have changed now.
b) There was zero contact with the opposite sex! While of course there is life outside school, I would prefer my child to have a broad experience including regular everyday contact with boys!!
c) It was too elitist (and I think this is borne out by some of Xenia's posts), in that academic and professional success were the be-all and end-all of existence.
This may all have changed since 20 years ago and of course this is only my personal view!!