Ruth Davidson, the leader of the Scottish Tories, said in a speech last night that it was time to 'clear the stables' in response to the recent allegations of sexual misconduct by politicians. The stables in the idiom allude to the Augean stables, those belonging to the ancient Greek mythological king of Elis, Augeas. These feature in the fifth Labour of Hercules. Hercules' task was to clean the stables, but this was no mean job -- there were a huge number of cattle in the many stables and the stables had not been cleaned for over thirty years. The task was set, therefore, in the belief that it was impossible, given that the stables were unspeakably filthy. Hercules succeeded by rerouting two great rivers, but Aegeas refused to hand over the reward he had originally promised.
The OED, at its entry for Augean stables, says of the idiom "Used allusively to denote any extremely dirty place, or (fig.) a place or institution characterized by great moral corruption or depravity".