As someone else said, we as a nation are pretty much forbidden to show our grief when something very bad happens...we are supposed to be upset for a little while and then pull ourselves up and get on with life.
Diana dying 'allowed' the nation to be upset and mourn in public and I think most people, if they looked deep down in their heart of hearts, weren't really crying for her, they were crying for all the people close to them that they'd lost. She's really a symbol of sadness, a marking post if you will.
Anyway, that's my ha'pennyworth.