For prestige, the most foolproof (yet by no means watertight - they could be being associated with more prestige by employers somewhere else) way is which high ranking universities have the highest percentage of privately educated students. Not only can this change around to some extent from year to year but Oxbridge are exempt from this because they deliberately try not to have the highest these days. The biggest thing I notice is that the privately educated are rating Loughborough better than the average person too. Some of the 'posh' love sport, for which it is perhaps too strongly known when it does much else, and Loughborough ranks far more academically high than many people (apart from those who know about Engineering) give it credit for.
The percentages are sometimes so relatively close that I'd rather tier them:
1 Exeter. Bristol (Bristol has clearly taken steps to increase non-private school admission and I feel it is no less prestigious than Exeter overall).
2 Nottingham (there was a time not so long ago when Nottingham would have been in tier 1. It still is for some courses). Birmingham. Loughborough
3 York. Leeds. Manchester (in some ways, Manchester is the most technically prestigious due to the number of Nobel Prize winners. But being more heavily associated with science can reduce appeal with the arty).
4 Lancaster
How does this compare to QS World University Rankings?:
32nd: Manchester
55th: Bristol
75th: Leeds
84th: Birmingham
100th: Nottingham
122nd: Lancaster
153rd: Exeter
167th: York
212nd: Loughborough
Exeter (30.3%)
Bristol (24.6%)
Nottingham (19.8%). Birmingham is about the same (said to be 'about 20%')
Loughborough (19.3%)
York (17.9%)
Leeds (17.7%)
Manchester (16.2%)
Lancaster (10%)