Through reputation, Warwick and UCL equate. Overall, they are academically stronger than that of Eburgh. However, Eburgh is fantastic too. I'd first say, that wherever you end up, you'll be coming out with a leading degree- in which case you should therefore look at the course structures and decide which one you love the most- and then get down to the nitty gritty. I think you should go for Wwick or UCL, because Wwick has a strong rep for the mathematical related subjects, and their course is much more open as all engineers do 2 years of pure engineering and in the 3rd year, you specialise- in which case, if after two years you decide you'd rather do mechanical than civil, then you won't be forced away into completing a degree you are not content with. UCL has a awesome, weird civil eng structure which is acc really different to other unis, and is extremely exciting.
Again, they're all so fantastic so I guess you should visit them all and decide what one suits you the best. Imo, i'd choose between UCL and Wwick. Good luck.