A bit of history. In 1894 it was decided by the case of Lemmon v Webb in the Court of Appeal [1894] 3 Ch 1 and then the House of Lords [1894] UKHL 1 that where branches overhang the land of another person then that person can cut back the branches as long as they don't enter the other persons land to do it.
This is because overhanging branches are a "nuisance" and you have a right to take steps to abate any nuisance that you are suffering.
Lemmon v Webb [1894] 3 Ch 1
Lemmon v Webb [1894] UKHL 1
However, if there is a Tree Preservation Order in existence then this takes priority unless the tree is causing actual damage to your property (eg subsidence).
There was a later case in 1919, Mills v Brooker [1919] 1 KB 555
In this case, the guy cut some overhanging branches from his neighbour's apple tree and sold the apples for a profit.
It was held that he had the right to cut down the branches but had no rights of ownership of the branches or apples growing on them. So, you can cut the branches down but you can't make use of them yourself. It was also stated that fruit remains the property of the tree owner whether it's still on the tree or is a windfall.
Perhaps part of the confusion about "must return" comes from the actual wording of the judgment in Mills v Brooker where it talks about the branches and apples must be returned or you may be liable for "conversion" of the apples and branches.
Don't forget that in this case, the guy was selling the apples so they definitely had a value.
Now one of the defences against a claim of conversion is that the original owner consented to let you have the item (the branches, apples or whatever). That is why people say that you must ask the tree owner if they want the cuttings back. If they decline then they have agreed to you having them. The cuttings then belong to you and it is up to you to dispose of them appropriately.