I voted the LSE, because internationally it's reputation eclipses Warwick's and domestically Warwick is arguably only known for 3 departments (maths, business and economics).
Oxbridge or nothing. Other universities are not in the same league as the Ivies.
Generally speaking, colleges like Harvey Mudd (the small, elite, liberal arts colleges that have a tutorial system like with Oxbridge) are the most prestigious in the US and most comparable in that regard. The Ivy League has great graduate programmes and lots of funding for interesting research but, like the LSE, the focus is very much on graduates. It seems they [LSE and the Ivy League, for instance]are more relatable than you think.