Bill visits Jenny's school and discovers she is missing class to go out with a boy with an interest in motorbikes. Bill's anger is tempered by the fact that she herself has accidentally met a mysterious young biker, who she finds impossible to dismiss from her mind.

Bill and Ben seem continually too exhausted from life to have sex. Ben insists on having Sunday lunch with his frilly-curtain-loving sister Tina and her boring husband Brian. After discovering David has sneaked a rat into her house a hysterical Tina slaps him, prompting an argument. Bill storms out of the house and drives David off in Ben's van. David reminds her, once they are speeding along that in her haste she has forgotten that she does not in fact drive. At that moment the biker appears beside her and talks her to a safe standstill. He disappears but not before Bill finds a note, apparently from him, giving a telephone number.

Forced by Ben's whim to unearth the garden barbecue, Bill accidentally pulls down the entire climbing rose display on Mrs. Grimes's house. During the hideous barbecue Ben reveals he has been summoned to the income tax inspectors, and Jenny turns vegetarian. While musing whether to ring the number she believes is that of the biker, now part of a huge papier-mâché dinosaur David has made, Bill is accidentally arrested in the supermarket for shoplifting. After returning home in triumph, she discovers the number is in fact that of a plumbing customer. Ben, meanwhile returns to reveal he has had a tax rebate.

Ben returns home with the first of his fads: a karaoke tape. His fun is short lived however when Bill's mother Bette arrives to attend the funeral of an old girlfriend from her youth, disrupting the household. Ben, out on a plumbing job, runs into an old girlfriend himself who seems to be very interested in him. When Bill discovers school has closed early she runs home from the bakery worried that Jenny and her boyfriend are alone in the house together. She is delayed by another meeting with the biker who chats with her about relationships, and then, remembering her worries rushes home and up to the bedroom to find Bette in bed with the widower. Mother and daughter talk about the difficulties of fidelity and Bill seems happier with her life with Ben. Ben, however is acting as if he has a secret to keep.

Ben is lying to Bill about strange assignations in a shady-looking lockup. Bill meanwhile is taking her driving test at last. A new sexist bottom-line-conscious manager at the bakery where she and Rona work complicates this. He forces Bill to take her test immediately after a dental appointment, when her mouth is still numb from the injection. Despite this, she passes, thanks in part to a fleeting appearance of the biker. In celebration Ben takes her bowling where they make a pact to force Ben to do all his own washing if Bill wins. Meanwhile, at home, Jenny reveals to Rona that her boyfriend has left her. Rona tells the story of her own teenage wedding which ended with her bolting from the church. Back at the lanes, Bill wins, and Ben takes her to the lockup to reveal his secret: a pale blue classic Chevy he has bought with his rebate money. Bill is not pleased.

Bill, having trouble driving a car the size of the Chevy meets the biker one more time. As she leaves we see the word ""Angel"" on the back of his jacket. After a run in with the obsequious Dawn, the bank teller, Bill returns to work for further confrontations with Rory, her boss, who implies that if Rona sleeps with him, he could make their lives easier. Rona wonders what to do. Meanwhile, Bill visits the home of Sammy, David's best friend, on a poverty-stricken Council estate and counts her blessings, while Ben has a heart to heart with his son about the facts of life. Later, when matters at the bakery come to a head, Bill and Rona resign in an unusual way. Back at the house, Ben bemoans the loss of Bill's income to the family and considers selling the car again. Bill realizes how much she loves him for all his faults and persuades him to keep it. The whole family goes to Battersea Park to take part in the Chelsea Car Cruise.