Not sure what you mean by a supervisory authority, but the Information Commissioner could be classed as one. I don't think there is an absolute requirement need to retain any of the docs, but it would be good practice for a PC to retain any correspondence it feels might need to be produced at a future date as evidence to settle dispute or to justify how it acted or made a decision. Storage need not be an issue if a competent Clerk can set up a decent Electronic document management system.