Angela Throgmorton's life is changed forever when a strange, scruffy, creature appears on her doorstep. Feeling sorry for the poor thing, she takes it in, feeds it and cleans it up. However, this creature is more than she can handle.
Told by her friend, Lavinia, that she and Old Tom should 'smarten themselves up', Angela takes Old Tom to the local department store to buy new outfits.
Old Tom is getting in Angela's way as she tries to tidy the house, so she suggests he goes outside and find a friend. However, outside Old Tom gets ruthlessly bullied.
Angela goes shopping for a playhouse for Old Tom and ends up buying an old rocket ship. Old Tom loves it and, with his best friend Lucy, they decide to fly it to Mars.
Lavinia decides to 'elevate the cultural tone' of Angela's household, by giving them regular musical recitals on her violin. Her talent, however, is negligible, and Old Tom and Lucy can't stand the racket.
Lavinia takes Angela with her to the beauty salon for a complete makeover. Angela is reluctant but agrees to go if Old Tom can come, too. At the salon, they are greeted by the temperamental owner, Istvan, who mistakes Old Tom for a hairy customer.
Angela tries to get her old car repaired but is talked into trading it in for a new car, instead. The salesman persuades Angela and Old Tom to test drive a sports car.
Angela is confined to bed after falling off the roof while retrieving Old Tom's golf balls. She suggests getting Lavinia to look after the house, but Old Tom offers to run the house instead.
Lavinia comes to take Angela golfing. Old Tom and Lucy want to go golfing, too, but Lavinia tells them the golf club won't let 'undesirables' play and they have to stay home.
Lavinia takes Angela and Old Tom to the town's finest restaurant. Old Tom is horrified when the owner, Chef Geoff, serves them tiny portions, so he takes matters into his own paws.
Old Tom is being pestered by a bird which has built its nest on top of Angela's chimney. The bird disturbs Old Tom's sleep, takes his food and fills the house with smoke.
Lavinia persuades Angela to buy Old Tom a computer, so he won't get up to mischief. When the computer arrives, Old Tom is more interested in playing with the box, so Angela tries the computer instead.
Lavinia thinks her nephew, Billy, is a brilliant artist and hangs one of his paintings in Angela's living room. When Lucy and Old Tom see it, they think Angela must be desperate for a painting.
When Lavinia discovers that 'the great example of modern art' was painted by Old Tom, she takes it to a local gallery owner who offers to exhibit and sell Old Tom's paintings and give Lavinia half the money.
Lavinia takes Angela, Lucy and Billy on a picnic. When they open the hamper, they find that Old Tom has hidden inside and eaten all the food. Lavinia is horrified, but Lucy suggests they can fish for food in a nearby river.
Old Tom is bored as his friends are all away - so Angela reluctantly sends him to summer camp. Old Tom settles in immediately and makes friends; however, Angela is concerned that Old Tom won't be able to cope without her.
While Angela is sleeping a couple of thieves sneak into her house and steal her antique vacuum cleaner. Old Tom sees them and hides in the back of their getaway truck, leaving a trail of sweetie wrappers behind him.
Old Tom overhears Lucy and Angela complaining about Billy, and mistakenly thinks they are talking about him. Devastated that not even his best friends really like him, Old Tom runs away from home and joins a circus.
While playing frisbee, Old Tom accidentally breaks Angela's favourite record by her favourite singer, Tom Moans. Old Tom and Lucy try and buy a replacement copy, but it's impossible to find.
Angela leaves Old Tom with Lavinia for the afternoon. However, Old Tom is very smelly so when Lavinia and Old Tom are invited to a garden party, Lavinia realises that she has to wash Old Tom. But this is not as easy as it seems.
Old Tom hurts his tooth on a lollipop, so Angela rushes him off to the dentist for a check-up. Old Tom's tooth will be fine, if he just gives up the sweet food.
A magician called Morton the Affordable, is entertaining Billy's party. Old Tom's antics disrupt the party, and Morton's assistant quits. Morton desperately needs a new assistant and he picks Old Tom.
Lavinia is organising a dance competition and wants Angela to take part. Angela, who loves dancing, is keen, but she doesn't have a partner. When Old Tom volunteers, Lavinia is horrified and tries to find an alternative.
Angela has organised a cruise on the harbour for herself, Old Tom and Lavinia. However, when Lavinia discovers the boat is an old rust-bucket, she refuses to join them and goes for a cruise on a sleek new yacht instead.
The Queen, wanting to see someone different at her next garden party, chooses Angela and Old Tom at random. Angela is delighted, but gives Old Tom a crash course in manners, just in case.
Angela bakes a cake to enter in the Home Appliance Show Bake-Off, but Old Tom eats it by mistake. Feeling guilty, Old Tom decides to bake a new cake to replace it.
Angela gets a job at a local sports store and takes Old Tom along. The store owner doesn't like Old Tom at first, but when Old Tom starts playing on the sporting equipment, he starts attracting so many customers.
Lucy enters a TV quiz show, so Old Tom helps her study. However, Billy is one of the other contestants and he tricks Lucy into catching the wrong bus. When Lucy doesn't turn up at the TV studio who will take her place?
Angela and Old Tom go to the local swimming pool where they meet Lucy who is practising for her swimming certificate. Billy is also there and starts to show off.
Angela and Old Tom go to the beach, where Old Tom gets involved in a sandcastle competition. While waiting for his sandcastle to be judged, Old Tom goes swimming and meets a baby whale.
Angela buys Old Tom a novelty radio, shaped like an apple. However, Old Tom, thinking it is an apple - eats it. All of a sudden strange voices start coming from Old Tom and Angela thinks Old Tom can talk.
Old Tom wants to play with Lucy but is not allowed to because she has chickenpox. Old Tom goes home and paints spots on his face so Angela will think he has chickenpox too.
Angela and Old Tom are planning to go to the zoo, but the car breaks down. As Angela tries to fix it, Old Tom is accidentally picked up by a garbage truck and deposited at the zoo.
Angela buys a house-cleaning robot, which automatically detects dirt and cleans it. Old Tom dislikes the robot - especially when it tries to clean him - but when it cooks Old Tom dinner, he and the robot become good friends.
Billy has a fabulous new tree house - complete with elevator - and all the kids want to play in it. However, when Billy refuses to let Old Tom in, Lucy decides to build her own with rubbish from the tip.
Old Tom and Lucy are practising for a go-kart race but Billy destroys their kart. Dismayed, they go home to Angela's place where they see a big box in the living room that looks perfect for a go-kart.