This the advice from the CAB Roots
If the roots of a neighbour’s tree spread into a property, they can be removed using the least damaging method available, unless there is a tree preservation order on it - see below. If a neighbour has to enter the tree owner’s property to do this, they must give reasonable notice.
The neighbour may also wish to consult their insurers, if there is a possibility that their property may be damaged by the roots. If the roots have already caused damage, the tree owner is liable to pay compensation but it must be shown that the tree owner knew, or ought to have known, of the danger.