Can anyone name this disturbing short film from the 90s?

Does anybody remember this short film broadcast on Channel 4 (I think) in the early to mid-90s? Here's what happens: a well-to-do white couple are completely devoted to each other and make a pact never to leave the other. All goes well at first until one morning they wake up only to find that their bodies are starting to fuse together. At first I think it's their fingers, then their limbs, and finally their faces. They frantically search for a way to stop the process but they are unsuccessful. The last scene is a close up of their heads joined at the cheeks, both with a terrified look in their eyes. It was quite disturbing and I have never forgotten it. I've performed loads of Internet searches but found nothing so far so any help is greatly appreciated. Cheers.