Yorkshire, 1947. Postwar Britain is undergoing Government-enforced austerity in the form of strict food rationing. Many people find this too much to bear, and resort to smuggling and even producing unlicensed black market meat and eggs.
But this is a risky business - butcher Medcalf is hauled off to prison after the police find a pig carcass hanging in the wardrobe. Over-zealous food inspector Wormold marks the meat 'Condemned' and paints it green, but Inspector Noble has the paint scrubbed off, so that he can have the meat for himself. Wormold spots flecks of green on meat he is served with, but his lover Mrs Forbes claims that it's spinach.
Apart from Wormold, virtually everyone is involved in the black market, right up to leading local dignitaries. Indeed, Dr Charles Swaby, accountant Henry Allardyce and estate agent Frank Lockwood are conspiring to hold a feast to celebrate the forthcoming marriage of Princess Elizabeth and Prince Philip. To ensure the success of this strictly private function, they have conspired with farmer Bernard Sutcliff to raise a magnificent but unlicensed pig, Betty.
Meanwhile, all is not well between Gilbert and Joyce Chilvers. He is a mild-mannered chiropodist with few ambitions, while she is a fiercely snobbish social climber - and they live with her increasingly demented 74-year-old mother.
Swaby, Allardyce and Lockwood drive to see Betty, and are alarmed to hear that she's injured her foot. Coincidentally, Gilbert is tending to Mrs Sutcliff, and after the others have left, Sutcliff asks him to examine Betty. He solves the problem but is now aware of her existence. Wormold arrives to examine Sutcliff's farm, but fails to find anything.
In response to Joyce's food complaints, Gilbert promises her pork every weekend - all he has to do is steal a pig. He regrets saying this, as she latches onto the idea. They prepare ingredients for its swill, incorporating rhubarb leaves and tin peaches - Joyce doesn't want to be thought common. After the scraps are delivered to Sutcliff, his boy Preston adds a freshly-caught rat.
Betty gets severe diarrhoea, something Gilbert discovers the hard way when he steals her in the middle of the night. When he brings her into Joyce's kitchen, she is horrified by the smell and mess, and orders Gilbert to kill the pig. When he refuses, she tries to lure it into the gas oven, but a neighbour smells the gas (and everything else) and comes round to investigate. Joyce blames everything on her mother, who is wandering around looking bemused. Later, Joyce tries to explain the pig situation to her, but is unsure that the message has got through.
Following the discovery of Betty's abduction, Swaby calls a crisis meeting. They realise that there is nothing they can do - they can't get another pig, as they're all licensed. Swaby considers that this is a symptom of Britain's decline, along with the newly-created National Health Service.
Wormold has an appointment with Gilbert, who is petrified that he'll discover Betty - but it turns out that he has no sense of smell. However, he can feel pain - something Gilbert exploits by stabbing him 'accidentally' in the foot when Betty wanders into the room, in order to distract him. After he leaves, Joyce orders Gilbert to strip prior to slaughtering Betty. Instead, he cuts his finger.
Veronica Allardyce complains about the smell at the Chilvers', where she has her piano lessons. Mrs Allardyce tells her to stop lying, but her father is intrigued.
Gilbert is approached by Allardyce, Dr Swaby and the rest of the conspirators. They go to collect Betty, but Joyce realises her strong position - she can blackmail them, but they can't arrest her. She serves cocktail snacks while Betty is slaughtered. The corpse is carried out dressed in a hat and coat. Swaby offers to arrange a home for Joyce's mother, and agrees that the Chilvers' can come to the private function.
The feast is held. Swaby proposes a toast to the royal couple, and later dances with Joyce. His hand strays - but Gilbert neither notices or cares, as he's rearing a new pig with Allardyce.