I am assuming you are asking for American views?
No single person can speak for all Americans and I noted you asked for individual opinions.
Here are the statistical facts about which UK universities that people in America search for:
- Oxford
- Cambridge
- KCL
- UCL
- LSE
- Edinburgh
- Imperial
- University of the Arts London
- Glasgow
- Durham
Although that can be said to be an indicator of popularity and familiarity, not necessarily prestige.
That said, one can get an indication of prestige by looking at the UK universities elite American students choose to go to by looking at this statistical fact:
http://www.nairaland.com/141689/rough-guide-best-most-reputable/9#13802115
- Oxford
- Cambridge
- LSE
- UCL
- Edinburgh
- KCL
- SOAS
- Imperial
- St Andrews
- London School of Hygiene and Tropical Medicine
Although it can also be argued that most Americans will not have the same views as their elite students, but on the other hand, ignorance about UK universities will be far more profound in the circle of most Americans than in sphere of their elite students.
You can also find a list of universities American students tend to attend by looking at this statistical fact:
https://www.britishcouncil.org/organisation/press/us-undergraduates-choosing-uk-their-studies
- St Andrews
- Oxford
- Edinburgh
- UCL
- Westminster
- LSE
- Cambridge
- KCL
- Glasgow
- University of the Arts London
It can be argued this is relevant because most people would tend to try and attend the most prestigious university to them they can get in or the most prestigious university for their course.
From these observations, you can form your own informed view and not have a view of “finger-in-the-air” analysis.