I think it’s generally a huge point of contention but imo:
Harvard - unmatched
Yale and Princeton is roughly equal to Oxbridge
Columbia, Penn and Brown are roughly equal to LSE and Imperial
Cornell/Dartmouth are comparable to UCL imo
I don’t think unis like Kings, Bristol, Warwick are anywhere near ivy in terms of prestige at all…these 5 are the only real unis I think that compare, but I’d love to know what you guys think
On what basis? If you’re into trying to rank, it’s already been done, and even USNWR (arguably more US biased than the others) rates U.K. universities better (and some ivies worse) than you do 
https://www.topuniversities.com/student-info/choosing-university/worlds-top-100-universities
https://www.usnews.com/education/best-global-universities/rankings
https://www.timeshighereducation.com/world-university-rankings/2020/world-ranking#!/page/0/length/25/sort_by/rank/sort_order/asc/cols/stats
Oxbridge isn’t even close to Yale/Princeton. Higher education in the US is literal marathons better than even the top foreign universities. It’s not even close.
It depends on your definition of “comparable”.
In terms of admissions, Oxford and Cambridge together admit over 6000 students per year in a country with one fifth the population of the US. So proportionately that’s more than the whole Ivy League. On the other hand, you only get in by being academically brilliant, not by being good at sport, doing any extracurricular activities or having a parent who works there, is internationally famous, or donates a building. And there is no incentive to choose a lower ranking university that offers you more money, since all universities in the UK cost essentially the same for a domestic student (in fact Oxbridge is cheaper than London overall, due to lower living expenses).
What that means is you get a much more concentrated group of really top students (if you took the top 100 students in their age group in the UK in any particular subject you’d find the majority of them in the same class at either Oxford or Cambridge) . Combine that with a single subject academic focus (which means you do about twice as many courses in your major in three years in the UK as you do in four years in the US) and the academic depth achieved by the average student at Oxbridge is far beyond that achieved by the average student at any Ivy League school (even Harvard, if you read some of the commentary by Niall Ferguson, see http://talk.qa.collegeconfidential.com/united-kingdom/2131394-oxbridge-admissions-criteria.html). In that light it’s not surprising that many academic rankings put UK schools so high in their list of global universities.
On the other hand, the Ivy League schools are looking for students who’ve achieved a lot of other things, and in many cases have wealth and connections that will make a huge difference to their (and potentially their classmates’) career. That’s not a comparable group of students or a comparable experience.
And why did you post this in the NYU forum?