I'm a first year at Bristol, and I would really really recommend you reconsider Bristol as an option. I had offers from Bristol & KCL, chose Bristol and haven't regretted it at all. I think when you are basing your choice on reputation there is hardly anything between the 3 uni's you have mentioned. There are people here who have had offers from both KCL and Durham and chose Bristol, as I am sure there are people at those uni's who have rejected Bristol.
I would say your choice should be based upon whether you want MASSIVE city = KCL, Big city = Bristol or tiny city = Durham.