I'm so sorry I couldn't post before. Uhm, it seems that nobody is getting close to the right name (and I helped by telling the story wrong at the beginning). So I'm developing the anecdote a little bit more:
An ancient ax was found in the place in which Alec Guinness and the star you have to guess were filming. For the next 20 years or so, these crazy people sent the ax to each other, in the most unexpected moments. One could enter his/her hotel room and find it on the bed, and hell knows how it got there.
#2: That way, when she was touring the US for some poetry reading sessions she founded the Indian ax in her bed. And when Guinness got an Oscar in 1980, she made all the arrangements at the Beverly Wilshire Hotel so when the proud winner entered to his room found the warrior ax on his bed. The actress loved this kind of tricks and word games.
Well, you also know, thanks to KC and Mythical Monkey, that is not Deborah Kerr, David Niven (now is obvious) or Laurence Olivier. Any ideas?