This is a synonym for an anus which is experiencing problems with producing solid stools (likely due to over-consumption of Yeo Valley yoghurt) and is producing faecal matter that looks more like a melt-in-the-middle
chocolate pudding than a healthy poo.
If you were to have sex with a
Chocolate Pudding Factory you would end up with your penis looking like a
chocolate pudding, hence the name. If you engaged in pegging with a Chocolate Pudding Factory you would likely end up with a Peg 'n' Pud.