Just realised I missed out the THE World reputation ranking in my list above of reputations/prestige rankings.
Surprisingly, or not so surprisingly, when I just checked the 2019 rankings, I find that it is 100% in alignment with the tiers I just created of:
Harvard, MIT, Cambridge, Stanford, Oxford > Princeton, Yale, Caltech > Columbia, Imperial, Cornell, UPenn, UCL >> Edinburgh, LSE, KCL >> Brown >>>> Dartmouth
So, I do strongly believe that is how, on aggregate, the world view these Top UK and Ivy League [Equivalent] universities.