The story
The term originates from Kelvin MacKenzie's time at the The Sun. His preferred description of the role of journalists when it came to public figures was to "stick a ferret up their trousers". This meant making their lives uncomfortable, and was based on the northern sport of ferret-legging. However, when it became clear that the tide of public opinion had turned against the paper's line, MacKenzie would burst from his office shouting "Reverse Ferret!"
Etymology from Wiktionary, CC BY-SA 4.0.