The big white rabbit is a character mentioned and appearing in The Secret Policeman's Ball 2006. Vince tells Howard about his game, Pelting the Rabbit in His Big White Face. He says that the rabbit can be stopped by pelting coins at him but if he catches someone he'll get them on the floor and Rabbit Rape them giving them a Terrific Bunny Bumming. Near the end of the show the rabbit appears and rapes Vince.
It is mentioned by Vince that the rabbit has a brother who's even more vigilant.