No planning permission is needed provided the height does not exceed 1 metre above ground level adjacent to a road or 2 metres elsewhere, and the gate, fence or wall is not within the grounds of a listed building.
If the erection of the wall, gate or fence encloses an area of land which facilitates a change of use then planning permission will be required e.g. if you extend your fence into a neighbouring agricultural field then this would be a change of use from agricultural field to private garden. This would require planning permission even though the fence may not.
See also Property Alteration Overview for more potential restrictions: https://planningaid.zendesk.com/hc/en-us/articles/203210341-Property-Alterations-Overview