We still do have fish kettles in Britain.  They are long oval pans which can sit across two burners - big enough to take 'the one that got away'!  \n\nThey have lids, and my stepmother's is a pretty fish kettle as it is shiny stainless steel.\n\nPerhaps the phrase comes about because one thing you would never do is cook two different types of fish in the same kettle as their flavours would taint each other.  Each has to be cooked (considered) separately.