I think if dry rot is spreading to your flat from another then they are causing you a nuisance. Thats a matter for your solicitor (may be different in Scotland!). Regarding the dry rot, the source of the original damp needs to be fixed and the structure dried out. This is best done with big fans as opposed to dehumidifiers. All infected timbers need to be removed and others treated to help prevent re infestation. New timber needs to be treated. If they are cut, the cut ends need treating before installation. All masonry walls near the attack need to be treated including stripping off plaster. If the moisture content of the timber is below 20% (I think) infestation will stop. ventilation helps if this is possible. Any concrete floors in the vicinity should also be treated.
It would be worthwhile checking your house insurance policy as they may cover this and pay for the repairs and alternative accommodation if necessary. They will then seek to reclaim this from the neighbour who caused the problem.