Still very perplexed by the mention of Copenhagen... Clearly the OP didn't like the fact that I pointed out that very few people would ever mention Copenhagen as one of the most renowned technical universities in Europe. No disrespect to Denmark (I have family there), but even there, DTU is better known as a technology institution.
Imperial formed the IDEA League a while back (although I noticed very little mention of it while a student there. I actually heard more about it from a German student from Aachen who I competed in a sports event with).
It includes a lot of the technology universities in Europe: Imperial, TU Delft in Holland, ETH Zurich in Switzerland, Aachen in Germany and ParisTech that joined a bit later.
Coincidentally, Paristech is the French attempt at creating an MIT although it is only comparable in name. Paristech includes a number of totally independent technical and non-technical universities in the Paris area. It was only created to improve visibility of the small, prestigious engineering (and business) schools in Paris. Actually any of these institutions are probably more prestigious than Imperial but they are much smaller: for example anyone who comes out of Polytechnique is likely to end up CEO of a large French firm by the time they're 40 (no exaggeration) whereas like myself, I know plenty of Imperial students who perform fairly ordinary, typical, albeit well-paid corporate jobs.
To this list, I would add TU Munich (and maybe even TU Berlin), EPFL.
As for the comment about "I'm not interested in crusty old buildings or snobby class-based elitism; but rather cutting edge facilities, sleek modern architecture and high quality teaching. I want to study somewhere renowned for attracting the most academically able students regardless of class or race. Basically somewhere like MIT or Copenhagen, but in the UK.", that may be incredibly naive.
Trust me, having lived in Cambridge in the US for a long time but also being an Imperial graduate, neither MIT nor Imperial are what I would call class-blind institutions. Imperial is incredibly upper middle-class like most top British universities. As for MIT, you'll find very few students who are from a poor background. Sure you get the odd "token" student that allows the university to present itself as providing equal opportunities. Overwhelmingly, students are from wealthy backgrounds. Even more so, when it comes to international students. These students certainly aren't from poor families back home. A lot are children of diplomats (so studies are paid), lawyers or directors of large firms.