To supplement the contributions above, the interviews are academic interviews (very different from US college interviews with alum). My D will be applying next fall (we’re based in the UK) and she’s already starting to prepare for interviews by deepening her understanding of her planned “major” (by reading books/articles, watching lectures, etc.).
As for other well-known UK universities, LSE probably tops the list for Americans. Other possibilities are Imperial, UCL, King’s College London and St Andrews.