Have your trees got a preservation order on them? You need to check this out. Even if they haven't got a preservation order some councils can say they must be kept because of their environmental value. However, if they are causing problems to your property, e.g. roots going under foundations or causing damp, then councils will usually consider granting approval for the trees removal.
Your neighbours might have not consulted with the council. However, most tree surgeons worth their salt will contact the council before they take down any trees in gardens to make sure it is OK to do so, otherwise they face really hefty fines.