I wouldn't discount Cambridge because of the college. Academically speaking, you will have pretty much an identical experience regardless of the college as lectures and course content is organised centrally. Lucy Cavendish also have some advantages, such as longer room lets.
Also, Cambridge Computer Science has a lot of Maths in it and this is coming from a Maths student, especially the theoretical Computer Science part. The Computer Science students also seem to have really good career prospects, especially regarding quant and other highly-competitive jobs. Jane Street, for example, now take more compscis than mathmos.
As for the other advantages of London, such as friends and things to do, I can't really advise you. The college system is really great for making friends but I don't know how important it is for you to already know people. I didn't know anyone originally and I was absolutely fine. There are also a lot of societies in Cambridge.
I wouldn't want to say which you should do either way but I wouldn't discount Cambridge immediately, and many of your advantages of Imperial also apply to Cambridge.