BTW, that’s how I would tier the UK uni as well:
Oxbridge, LSE, Imperial = Ivies/equivalents
UCL = UMich/UCLA (solidly near-Ivy and close to the Ivies/equivalents)
Edinburgh/Warwick/St. A’s/Durham/KCL = UT-Austin/NYU/W&M/UNC/USC/UW-Madison (near-Ivy or close; some departments highly-esteemed, some not so much; entry requirements may also vary by subject and there may be a mismatch between entry requirements and faculty reputation).