jno - "given that you can go on adults-only cruises, I'm not sure why it whould be legal to discriminate against children (and their parents), but not against unmarried people or gays or Irishmen (etc). Are some protected species and some not? That seems discriminatory in itself."
That comparison is not actually valid in my view.
'Adults only' cruises are geared specifically towards adult passengers - and on-board entertainment is geared to that clientele, without specific childrens' facilities - play areas, creches, and appropriate crew.
But - and this is where the analogy falls down, I don't believe that any line would turn down a family with children on the basis that they were not an adults-only party, or that passengers with no children would be prevented from cruising on a 'child-friendly' voyage.
Furthermore, from my experience, Cunnard and P &O both offer identically designed ships and itineraries - one for families, and one for adults, so a fair choice is available - not a choice offered by discriminatory hostelry owners.