Many trees are protected by a charge called a Tree Preservation Order (TPO). This means that you will need permission to prune or fell a tree. A tree can also be protected if it is a designated conservation area or other designated areas. Removing a hedgerow may also require permission.
If in doubt about whether your tree falls under a TPO or is located in a conservation area contact your local council's planning department. Please note there can be heavy fines imposed if you prune or fell a tree within one of the above areas.