The only difference I can see is that in Scottish law the branches are presumed to have some value and are considered the property of the tree owner, and must be returned to him, unless he says he doesn't want them.

From http://www.treewarden.org.uk/treelaw.htm (The site is sponsored by the City of Edinburgh Council):

Branches:- The title of a property includes not only the soil on which the property stands, but also all that is above and below it. With few exceptions (e.g. passage of aircraft) the owner is therefore entitled to the uninterrupted right of the air above the land. On this principle, therefore, the branch of a tree which overhangs a neighbour's land is an infringement of his rights, and, although it may cause no actual harm, is considered in law to be a special kind of nuisance. The tree owner is not obliged to cut back the overhanging branches, but the person whose property is overhung has the right to cut back the branches to the boundary to remove the nuisance. This is known as abatement (care is needed if the tree is protected, see Tree Preservation Orders). Although there is no obligation to ask the owner's permission or give notice of any intention to cut back, it would be good neighbourliness to discuss the problem in a friendly way with the owner first - it may be possible to obtain help or agreement to remove more than was envisaged.

If pruning is carried out without the owner's permission it is important not to enter property, or for equipment to cross the boundary - for example it may be illegal entry to lean a ladder against the trunk of a tree as an aid to cutting a branch if the trunk is on the other side of the boundary. Even after removing branches, the prunings remain the property of the tree owner and therefore the branches, fruit, leaves and cones cannot be put to use without the owner's permission. To do so would constitute an offence known as conversion i.e. appropriation of the owner's property. Nor should material simply be burned or disposed of because it appears to be of no use. The material may be returned to the owner's property, but if doing so causes damage (e.g. by throwing branches over the fence and damaging the owner's conservatory) there may be a liability to pay for the damage. But if the owner gives notice (preferably in writing) that he does not want the material then it may be disposed of. However, there is no precedent for recovery from the owner of the expenses incurred in disposing of the residues.