In the United Kingdom, you have the right to prune or remove branches from a tree that are overhanging your property, as long as it is done in a reasonable manner. This is known as the "right to abate a nuisance." However, before you take any action, it is always best to first discuss the matter with your neighbor and try to come to a resolution that is mutually beneficial.
It is important to note that you are not allowed to enter your neighbor's property without their permission to prune or remove the branches. Additionally, you should be careful not to damage the tree or any of the surrounding property while you are working on it. You are also responsible for disposing of any branches or debris that you remove.
Furthermore, it's important to note that if the tree is protected by a Tree Preservation Order (TPO) or if the tree is in a Conservation Area, you will need to apply for permission from your local council before carrying out any work.
It's also worth noting that if a tree is causing damage to your property and your neighbour is refusing to deal with the issue, you may be able to take legal action against them for the damage. In this case, it would be wise to seek legal advice.
In summary, while you do have the right to prune or remove branches from a tree that is overhanging your property in the UK, it's important to approach the situation in a reasonable manner, always discuss with your neighbor and obtain any necessary permission. It's also good to consider the tree's preservation status and the potential damage that the tree may cause to your property.