Uncertain, probably from po, abbreviated slang based on French pot de chambre (“chamber pot”), after the distasteful expression anyone would adopt upon being presented with a full one. Perhaps similarly from pooh; perhaps influenced by poker-faced. Also possibly “poor-faced”.
- (Britain) Wearing a particularly stern and disapproving expression; humourless; priggish. [from 1930s]
- (Britain) Poker-faced.