Before the film
In the film, "everyone in the apartment is ill" because of a mysterious disease which has broken out and makes the victim go pale and vomit and have hallucinations. Towards the end of the film, it is revealed the disease could have come from a secret laboratory harbouring experiments on monkeys but this is dismissed as implausible.
In the film
The zombies first appear before the proper outbreak when Shaun notices disturbing things; such as a man frantically running away from something or someone; and another man on the sidewalk picking up a pidgeon and seemingly eating it. Later when he is dumped he goes out with his friend Ed and they see a shuffling man come up to the pub and knock on the wall but the owner tells him they're closed. This zombie goes unnoticed. Previously, another infected woman on the bus had been coughing onto Shaun, disturbing him. Later when they leave the pub, Shaun and Ed see a shambling man come up to them very slowly, moaning. When they try and get him to do karaoke with them, the zombie just groans, and Shaun says "What's up with him, he should say base!" Then they both run.
In the morning Shaun goes out to empty streets full of signs of damage. Then he comes upon the first zombies - who still look so much like people that he seriously thinks they're just hung over from the Sunday night before. He is much quicker than them, meaning that by the time he has bought an ice cream and left the shop, the zombies are still shuffling up to the shop itself. When he gets home, he watches several conflicting TV programmes that relate the outbreak. Then he sees Ed at the window who tells him of a girl in the garden.
When they investigate the girl, Mary, they think she's drunk because of her glazed expression and her intrusion. But they soon come to their senses when Ed accidentally impales her on a stake. She still rises to her feet, shocking them. Thern another fat zombie comes in and him and Mary attack. Shaun and Ed fend them off and eventually kill them.
When they're watching more channels, the newsreader says to keep all your exits blocked, and Shaun notices the door is open. Suddenly, a zombie with one arm comes in through the door, and they kill him too.
The zombies converge on their location (perhaps drawn from all the shouting) and then they prepare to leave. Shaun goes to the toilet and suddenly notices Pete, their flatmate, is a zombie. He had been "mugged by some vandals" the night before and one bit him. Now realizing that this is serious, Shaun immediately leaves, but not before telling the zombie Pete that they're off to the pub.
When on the run Shaun and Ed go to Liz, Shaun's ex-girlfriend, and her family, as well as his semi-friends David and Dianne. Zombies are converging in their apartment and Shaun notices that their weakness is being hit on the head. He gets Liz and David and Dianne out and then they go to his mother's and his step-father's. Shaun's step-father has been bitten and is slowly succumbing. In the car, he finally succumbs and reanimates. Shaun's mother doesn't think there's anything odd, but Shaun tells her that it isn't her husband. They run away from the zombies and get to a safe place.
But the road to the Winchester pub is surrounded by zombies, so they pretend to be zombies to get through, which fools the zombies, until they notice they are human. Then Shaun distracts the zombies by luring them away by saying he's a "free buffet."
Shaun turns up again later when the rest are arguing. David goes to the basement and notices the zombies have returned. Then Ed turns on the jukebox and attracts the zombie barman, who they defeat, but more zombies break in. The zombies attack, and then Shaun's mother reveals she was bitten. She dies and reanimates. Shaun has to kill her before she kills him, and then the zombies pull David out and eat him. Dianne runs out and gets killed. Then the zombies follow them down to the basement, cornering them, but the Army comes in at the end and guns down the zombies.
Later on the surviving zombies have been turned into slaves and made into supermarket workers.