On face value a basement extension could be argued to meet the description of “the enlargement, improvement or other alteration of a “dwellinghouse” in Part 1 Class A of the Town and Country Planning (General Permitted Development) Order (GPDO) 2015 and thus that it benefits from permitted development rights provided the proposal meets the criteria set out in Class A.
However, a High Court judgment (Eatherley v London Borough of Camden, December 2016) ruled that the basement extension in question could not be lawfully carried out using permitted development rights as the proposal comprised engineering works which were deemed a separate activity in their own right not benefitting from permitted development rights.
The ruling does not mean that all engineering works required to facilitate basement extensions will require planning permission but it does bring the issue into question so you need to be careful when planning an extension of this kind. As a result of this case, the London Borough of Camden issued an Article 4 direction to remove all permitted development rights for basement extensions. Other local authorities may have similar restrictions in place.
If you are planning a basement extension, you are therefore advised to contact a chartered town planner or your local planning authority.