According to "Story Of The Scene: 'A Private Function', Malcolm Mowbray, 1984" published in the April 25, 2008 edition of "The Independent", "(Dame) Maggie Smith found herself obliged to vault over the back of one porker when she was hemmed in during one kitchen scene, and everyone on-set was traumatized by their earthy nature." The pigs used in this movie were "unpredictable and often quite dangerous."
According to Sir Michael Palin, this is the only movie ever to credit a "Bucket Boy". During filming, the crew were having difficulties dealing with the pig defecating on-set. A young man was hanging around near the set, saying he'd "do anything" to get into movies. They invited him on-set, gave him a bucket, which he was to hold under the pig.
For the scene toward the end where Betty the pig needed to travel in a car, she would not initially get into the vehicle. The set-up required her to ride in the back seat, but when she did get in, she then jumped into the front seat, and onto the lap of Sir Michael Palin, who stunned, sat there grinning.
Intellectual Animals U.K. advised Producer Mark Shivas to use pigs that were female and only six months old, as male pigs might be too aggressive, and older pigs were much more difficult to handle.
The script took three years to complete.