Singing in the Shrouds by Ngaio Marsh

All aboard for murder The Cape Farewell steams out to sea, carrying a serial strangler who says it with flowers and a little song. Behind, on a fogbound London dock, lies his latest lovely victim; and on board, working undercover to identify him before he strikes again, is Inspector Roderick Alleyn. But-with a collection of neurotic, bombastic, shifty, and passionate passengers at one another's throats-how long can he keep the investigation on course?

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ONE FOGGY NIGHT...
in the gloom of the London docks, a policeman hears some strange singing and comes upon the dead body of a beautiful girl. She is clutching a piece of an embarkation notice for the Cape Farewell, bound for South Africa.
As the ship heads seaward, Superintendent Alleyn that suave and observant gentleman from Scotland Yard comes quietly aboard in search of the killer...
The 'pleasure' cruise that follows is calculated to keep any reader on the very edge of his deck chair for suspicion is widely scattered among a fascinating set of characters. Suspense mounts sharply and in order to finally solve the puzzle, Alleyn is forced into one last desperate play when
HE SETS THE STAGE FOR THE MURDERER TO ATTEMPT ANOTHER KILLING...
'In her ironic and witty hands the mystery novel can be civilized literature.' -New York Times