I remember seeing that one too, JoanK, long ago. Wasn't it a made for TV movie? I couldn't remember who played other than Angela Lansbury so I looked it up.
What a cast. Aside from Lansbury and Taylor, Geraldine Chaplin, Kim Novak, Edward Fox, Tony Curtis, and Rock Hudson appeared. Two other names I recognized on the list were John Bennett, and Charles Gray. Gray played Mycroft opposite Jeremy Brett and Edward Hardwicke in their TV Sherlock Holmes series. I last saw Bennett in one of my favorite fun SciFi films, The Fifth Element. Pierce Brosnan was listed as "uncredited". Did you notice him? I am going to have to find a copy to watch.