Garden waste can build up over time and become problematic. It may be possible to compost some, but not all materials are suitable for rotting down and making into compost. You also may end up with too much and the last thing you want is an overflowing compost bin.
If you want to get rid of garden waste, the easiest way is to order a green wheelie bin from your local council. You will be able to put all garden matter into this bin to be taken away, usually in bi-weekly collections.
In some areas, it will not be possible to get a wheelie bin specifically for garden waste. You may have to take your waste to a recycling plant. There are some that are approved by the Environment Agency, though it will usually cost money to leave waste there and you will have to be approved. If someone else is doing your gardening, ask if they can dispose of waste for you.