The best non-oxbridge universities?

Hi,
For computer science, I know oxbridge and imperial are generally classed as having the most rigorous and prestigious courses. What would you say is the group of universities that make up the next tier of universities after them? Obviously, I know this varies, but in terms of reputation, prestige and a challenging course, what would you say?

Bristol, Edinburgh, Warwick, and Manchester spring to mind. That's not to say the ones I haven't named aren't any good.

(I go to Edinburgh so I might be slightly biased)

Thanks for the response. Would you say the UCL course is as good or is it not the best place for computer science?
Also, I'm thinking of applying for the Edinburgh course, how do you find it? I'm thinking on applying for second year entry but do lots of people do that or is it a bad idea?