This is a Land of Confusion
I have no idea how this conversation originally came about -- either we were talking about Phil Collins or puppets, but somehow I ended up watching this:
Land of Confusion was the fourth single off Genesis' 1986 album, Invisible Touch, and the video, as you can see, features puppets from an 80's satirical sketch show called Spitting Image.
The show was pretty popular in the 80s and 90s, even though the puppets - caricatures of celebrities, politicians and the Royal family - looked like what my nightmares are made of.
Phil Collins saw his image used on the show one day and approached the creators Peter Fluck and Roger Law, to create caricatures of the entire band, and help "staff" a video.
The Land of Confusion vid got a lot of airtime on MTV and stars Ronald and Nancy Reagan, Benito Mussolini, Muammar al-Gaddafi, David Bowie, Mick Jagger, Johnny Carson, and Leonard Nemoy, to name a few.
I got watching a few clips from Spitting Image, and it's pretty cheeky.