Louis D'Ascoyne Mazzini (played by Dennis Price) was raised by a mother obsessed with the rich and titled family that had abandoned her when she eloped with an Italian opera singer. In his turn, Louis becomes obsessed with fulfilling her dying wish to be buried on the family estate. He is, after all, eighth or ninth in line for the Dukedom - if only all those intervening family members would die. Initially his interest in that idea is passive, but a chance encounter with one of the family members brings him to the conclusion that causing a death or two would be quite alright. There's also a substantial story line about his dalliance with a beautiful young woman - he proposed to her but she turned him down because he was too poor, instead marrying rich and boring. So now she visits him on the side.
I don't know that I ever laughed out loud, but I grinned through huge portions of the movie. Price is so casually and charmingly evil, and the variety of Alex Guiness' that he offs (in so many different ways) is just marvelous. And the punchline is both ironic and funny. According to Wikipedia this movie is on at least two significant "Top 100" lists (Time and the British Film Institute): I found it a little light-weight for that, but it's definitely a lot of fun.