No-one is entirely sure why so many trainers have apparently been slung over the branches of this tree, but an article from The Argus (see link below) offers a few suggestions. One person suggested that, as the tree is very near a skate park. it could simply be that, having worn their trainers down from months of skating, the youngsters decided to toss them in the tree instead of the finality of throwing them away.
Another suggestion is that it is a type of a memorial to someone who died in the area. This is similarly to a gang-culture tradition born in the US where the members of a gang would throw shoes into a tree if one of their own had been killed.
Other Brightonians have offered the idea that it is artwork linked with the graffiti in the lanes and others have suggested that it is a sign saying that that spot is where you need to go if you want to buy drugs (to be honest as it's next to a skatepark, you don't really need a tree full of trainers to tell you that).
( http://www.theargus.co.uk/news/8768300.Brighton_tree_full_of_trainers/)
So, the mystery remains unsolved, which I kind of prefer as it makes it another quirky, unusual element you can always find around Brighton.