Many trees are protected by tree preservation orders which means that, in general, you need the council's consent to prune or fell them. In addition, there are controls over many other trees in conservation areas.
If you are unsure about the status of trees which you intend to prune or fell (or you simply require further information) you should contact your Local Planning Authority.
The use and nature of hedges can be controlled through planning conditions and legal covenants.
You don't normally need permission to plant a hedge in your garden. And there are no laws that say how high you can grow your hedge.
However, you are responsible for looking after any hedge on your property and for making sure it is not a nuisance to anyone else.
If a hedge does adversely affect the owners/occupiers of an adjoining domestic property then they may be able to take action through the High Hedges complaints system introduced by the Anti-social Behaviour Act 2003. The complaints system specifies the type of hedge and the adverse effects that it covers and, if you have concerns about the effect a hedge is having on your property you should contact the your council to see whether the High Hedges complaints system is applicable to your circumstances.