You need to see if your tree is protected by a Tree Preservation Order (TPO) or is in a conservation area before carrying out any work.
This includes any work to your neighbour's tree, which you are allowed to cut back to your property boundary.
Work to a tree with a TPO
You need to apply for permission to do work to a tree with a preservation order.
Your application will need a site plan that shows where the tree is on the property. If you are carrying out the work because the tree is diseased or damaged then you will also need to provide a tree survey, which you can get from an arboriculturist.
Before you apply read the Planning Portal's guidance for tree work applications. This will help you describe the work you are doing which will make it more likely that your application is accepted.
Apply to do work to a tree with a TPO
Work to a tree in a conservation area
If your tree is more than 75 mm wide at 1.5 metres tall then you will need to give us notice of any work you want to do.
You will also need to provide some photos of the tree when you apply.