A famous movie actress is found dead, washed up on the shore of Kent. The only thing to indicate it might not have just been an accidental drowning is that the police found a button from a dark overcoat tangled in her hair. But, virtually no one knew that the actress was at this isolated cottage, save for her husband, apparently a fellow actor, and the young man she picked up off the street to spend some time with her (but all on the up and up: no funny business, so to speak).
Inspector Alan Grant from Scotland Yard gets the case. He is showered with red herrings, but gets his person (one needs to be gender neutral in these things, right?) in the end.
Not a great story, and some of the action doesn't always make the best sense. But the characters are well drawn and the overall story line is engaging enough to keep one's interest the whole way through.