Oxbridge
Imperial
UCL
LSE
Edinburgh for medicine and vetmedicine only.
KCL and Barts for medicine and dentistry only.
RVC for vetmed obvs.
Perhaps Warwick for Mathematics/Economics/Business/Finance etc. Perhaps. Perhaps.
These places above are Tier 1 maybe verging on to Tier 2 as the Americans say. Comparable to the Ivies, Stanford, Berekeley, MIT and Caltech etc. (Edinburgh Medicine is comparable to UPenn Medicine for example).
that's it IMO...everything else tries to be 'elite' as the OP said but they don't really carry the same weight as these institutions. I know some arty farty person will say that Durham (and its pathetic 'comparable to oxbridge' collegiate system) carries weight - maybe it does. I would say between tier 1 and tier 2.
I notice places like Bristol, Exeter, St Andrews and Edinburgh (except for medicine) especially are typically for the public schooled 'clever but not that clever' people who wanted to go somewhere 'good but not elite'. These are deffo tier 2 institutions - like NYU or Washington lol.
Places like Birmingham are just plain run of the mill mediocrity (apart from med and dent). Universities like that are in reach of the general population (not the elite), thus anyone can get in. Tier 3.
Tier 4 are places like Manchester Met or even Oxford Brookes. Now that is going to university just for the sake of going to university. LOLZZZZZZZ