Sometimes trees are protected and can be subject to a Tree Preservation Order (TPO). In such situations, the council is in control of the tree work involved and it is an offence to undertake any such work without the explicit permission of the relevant council.
Please click the below links for more information in your area and how to apply for permission:
Derbyshire: Tree Preservation Orders
Oldham: Protected Trees
Stockport: Tree Preservation
Trafford: Tree Preservation Orders