We lived in a conservation area, not only were trees protected but also certain hedgerows. These were listed in the conservation details. The only trees that you were allowed to lop without permission were fruit trees. Your best bet is to get your local council involved. we had something on the same lines happen a few years ago. We had a pair of Old Yew trees either side of our driveway, in a conservation area. Our new to be neighbours put in planning permission to have one removed. This is before they had even completed the house purchase. The first we knew of it was a planning notice on the tree. However, to cut a long story short, we eventually got a Tree preservation order on both Yew Trees which at the time were estimated to be 350 years old, approx same age as cottage. Countact the Council , they will have an officer who deals in this area. Is the tree of pacific interest, aged, rare, unusual specimen etc? Any of this would help your case . I know that cutting down or lopping trees with TPO's is finable, not sure if same applies to conservation areas.