To be honest, this is only undergrad, so if you're planning to go on to further study then it probably doesn't matter from a reputation point. I don't know much about the London Unis, as I didn't apply to any (I live near London, wanted to spend at least three years somewhere else, even if I return for postgrad), but Durham is very good for philosophy. A lot of people put Durham down, saying it doesn't deserve the reputation it's got, but most people will admit that it is good for some subjects - philosophy is one of them (It's recieved full marks on teaching for the Times Guide for at least the past few years, and that's really the important part IMO).
I'd base your decision more on where you think you're going to be happiest. If you like clubbing etc, go to London - you won't get a better place anywhere. If you're not into that kind of thing, you might prefer Durham. Visit them both and then decide. From a reputation point of view I really doubt it will matter, so just go with more where you can see yourself for three years. Of course, I'm probably biased because I'm thinking of going to Durham for Philosophy.