The use of fish as a decorative feature on a punch bowl is not, at first, an obvious choice. Although sometimes drunk with anchovy toasts, salmon, fried whitebait or oysters (in Britain at least), this does not seem to be the reason for fish decorations.
Instead, it appears that the use of fish decorations on British punch bowls was associated with alcohol and the imagery of being as drunk as a fish.
The expression ‘to drink like a fish’ has long been popular in Britain to indicate drinking a large amount of alcohol. It was first recorded in 1640, appearing in Fletcher and Shirley’s stage comedy The night-walker, or the little theife: ‘Give me the bottle, I can drink like a Fish now, like an Elephant.’ In William Congreve’s 1700 play The Way of the World, he says ‘Thou art both as drunk and as mute as a fish.’