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 alterations and permitted development for more potential restrictions.