Bath and North East Somerset Council says it can make a tree preservation order to protect trees which are an important part of the amenity, or the public use and value, of a place, and that once one is in force it is an offence to cut down, top, lop, uproot, wilfully damage or destroy the tree without the council's permission.
On conservation areas the same council says that if you live in one and you want to reduce or fell trees you will need to notify it six weeks in advance of the planned work, applying through the standard planning application process on the Planning Portal, and it warns that it is an offence to fail to notify it.
On front gardens the Planning Portal says planning permission is needed where a new or replacement driveway of more than five square metres uses traditional, impermeable surfacing that does not drain to a permeable area. The same page says permeable or porous surfacing, or rainwater directed to a lawn or border, is the route that does not need an application, and that the permitted development allowances apply to eligible houses, not to flats or maisonettes.
We would explain how you check the conservation boundary, any tree preservation order, any Article 4 direction and the proposed work before confirming whether permission or notice is needed.