I know of two trees at opposite sides of the Dales which locals refer to as a Wishing Tree. These tangled roots are just a small part of an oak tree, on the river bank in Masham. I'm not sure exactly how you're supposed to use this one, but all sorts of treasures and wishes could be left, and found, within the lower branches and roots of this lovely old tree.
The other well-known Wishing Tree is in Flinter GIll, Dent, where you can also find the Dancing Flags, flat limestone blocks where weavers (and maybe also the Terrible Knitters of Dent) laid out their woven fabric and walked over it in the shallow water to make a kind of felt. When you get to the Wishing Tree a little further up, make sure you walk three times clockwise through the tunnel formed by the tree roots to make your wish come true.
There are other ways to make a wish upon a tree, including sticking a coin into an old money tree such as the one on the Bolton Abbey Estate, following a custom that's thought to date back to the beginning of the 18th century. Apparently at that time people thought if they were sick and a coin was pushed into the trunk, they'd be cured as the illness would then be transferred to the tree. I think there's another coin tree by Clapham Beck and I think I remember one of the Ingleton Waterfalls Walk too.
We quite often talk about 'knocking on wood' to bring us good luck. There are different explanations for why we do this. One is from pagans who thought mystical creatures made their homes in trees and could be woken with a knock on the tree to make a wish. Others believe that by touching wood, you are touching the wood of the Cross and seeking protection from God.
Whatever the reason, trees (preferably live) can definitely make us feel better. I love my two talking trees.