Although there is no formal qualification required to carry out PAT testing, the operative must be competent to do so & this includes both 'knowledge' & 'experience'. Competency levels will differ depending on the type of equipment you are testing.
For example, an operative testing a handful of PC's in their office would require a different competency level to that of an Electrical Contractor that could up against a variety of equipment types in any type of environment. The IET Code of Practice does offer some basic guidance levels for competency requirements.