Do I need Building Regulations approval to erect a garden wall?

No, but any external lighting or power points will unless they are installed by a registered electrician. To ensure the electrical installation meets the requirements, it is suggested that the services of a qualified electrical contractor be employed who is registered on a self-certification scheme for Part P of the regulations (Electrical Safety) and is able to provide you with an electrical certificate which confirms the design installation and testing of the system is in accordance with British Standard 7671.