Property constraints
Listed buildings, designated land and other protected contexts can alter permitted-development rights.
For homes in England, the answer depends on whether the pool is outdoor or within a new building, the property and location, and whether permitted-development limits and local restrictions apply.
Planning Portal says outdoor domestic pools often do not require a planning application when they meet permitted-development rules for incidental residential use. Those rights have limits and conditions, so the fact that a pool is in a garden does not automatically make it exempt.
An indoor pool can involve two linked questions: the pool itself and the building that contains it. Planning Portal says a pool hall may be treated as an outbuilding, while building-regulation requirements can also apply to the building, ventilation and thermal performance.
Listed buildings, designated land and other protected contexts can alter permitted-development rights.
Local planning authorities can confirm whether restrictions, Article 4 directions or project-specific issues affect the site.
They are different systems. A project can require one, both or neither depending on the work. Building control should be checked where a new pool building, structural work, services, ventilation, heating or other regulated work is involved.