It's probably the highest brow of the mainstream (ie, non FT) newspapers. It's seen as less try hard and pseudointellectual than the Economist i think.
Depends what topic you're going for but the guardian or ft, tatler, London or new York review of books, times literary supplement etc would be found in eg a London club library. Economist too, it's a light but fun read.
I'm British, have read the Economist in the past and a friend of mine interned there. I think "middle class" is bang on to describe their audience, which ranges from aspirational students to working professionals who want a quick news summary with some wit. Not many builders (working), dukes (upper) or Oxford faculty (upper middle) would be caught reading it. It's definitely seen as middlebrow fodder for undergraduates.