When Hercules the horse dies Albert takes to his bed. Harold buys another horse which he names Samson, but then this horse also appears to fall ill. When Albert gets up to tend to the horse he finds out that the illness is actually a pregnancy and Samson is a mare after all. Rather than call her Delilah, the name Hercules II is chosen.
Timothy Stanhope,an elderly antique dealer, comes to the Steptoes' yard. He is a cultured man and Harold sees the opportunity to make a friend with whom he can converse about the finer points in life. Unfortunately he has not twigged that Timothy is gay and wants him for more than erudite conversation. Albert has but Harold ignores his father's warning and goes to Timothy's flat. He soon comes back again.
When heavily pregnant Daphne comes to the yard looking for Harold, whom she suspects is the father of her baby following a one night stand at a party, Albert tries to get rid of her. But Harold warms to the idea of being a father and Albert becomes proud for his son. Unfortunately it turns out that Harold is not the father after all, another party-goer called George is, and he asks Harold to be best man at his wedding to Daphne. Albert does his best to comfort his disappointed son.
Sick of watching his old monochrome television through a magnifying glass, Albert wants a colour set but Harold uses the money to buy a sports car to take new girl-friend Muriel to Brighton. When Albert wanders off and ends up in hospital suffering from amnesia, Harold sells the car and buys a colour television instead to jog Albert's memory when he takes him home. But Albert seems to remember quite a lot as it is.
Albert has been coughing a lot and Harold accompanies him to the hospital where they both submit to having X-rays taken. Whilst Albert gets the all clear there is an unusual growth on Harold's X-ray and tuberculosis is suspected. However it turns out to be a necklace that Harold was wearing that showed up on the X-ray and he is cleared.
With the lease on their house about to run out Steptoe and Son visit their local bank manager to arrange a loan and over-draft facilities. He is quite agreeable but insists they wine and dine him and his wife at an expensive local restaurant. Harold gets ever so slightly overdrawn as a result of buying the food but unfortunately Albert's usual lucky touch deserts him at the gaming tables when he tries to recoup the rest.
Albert accidentally knocks over Harold's china cabinet, smashing its contents. Scared to face his son he hides the broken pieces along with other items, knocks himself unconscious and claims he was robbed by five skinheads and a Pakistani. Harold calls the police who commend Albert on his bravery in tackling the intruders. He is even awarded a medal. It looks like he might just have got away with it until Harold looks in the old gas cooker and makes an unwelcome discovery.
Harold wants to win the affections of a woman called Jean who is a great fan of ballroom dancing but is pessimistic because he has two left feet. Albert, on the other hand, was once very light on his feet so he teaches Harold the basic steps with which to impress Jean. Unfortunately Albert has been leading all the time and Harold going backwards so he ends up only learning the woman's steps.
Harold is predictably displeased when Albert announces his intention to marry again, but he is shocked when he sees that his prospective stepmother, Daphne, is a woman he went out with himself many years earlier, losing touch with her due to a misunderstanding when he joined the army. Daphne and Harold's old feelings for each other come back immediately, leading Daphne to make a hard decision and give up both Steptoe and Son.
Campaigning for the by-election has started and, despite his failure to be selected, Harold is still a Labour supporter whilst Albert is voting Tory - not only that but Prime Minister Heath is coming to tea with him. Harold is appalled and plans not only a nude protest for the photo call but a nasty surprise in the toilet which is unfortunately discovered by the Tory agent when he comes to announce that Heath's visit is off.
Harold wants to move up in the world so he and a reluctant Albert go to view a suburban semi-detached house. When the local Residents' Association gets to hear that two rag and bone men are planning to move into the area they offer a bribe to stop them coming. Harold is appalled by such prejudice but Albert sees a potential money-spinner on the way.
After suffering the results of his father's cooking, which involves crimping pie crust with false teeth, Harold shows off his new purchase, a huge snooker table, so big it eventually ends up in the yard. When he finds that Albert is much better at the game than him he becomes obsessed with the notion of beating him just once in his life and makes his dad play snooker in a rainstorm in the middle of the night. Finally a jubilant Harold wins. . .. Or was it Albert's trick shots making him think he'd won?
Having rescued Albert who's got tied up in knots doing yoga, Harold crows over his latest purchase, a Regency commode bought for seven pounds from a woman who wanted rid of it. Then her husband arrives, accusing Harold of taking advantage of his wife's ignorance and offering to buy it back for a hundred and fifty quid - which Harold accepts. After he has gone, an antique dealer arrives and goes into raptures over the commode, offering six hundred. However Harold has to buy it back from the irate spouse at three hundred. Albert points out to him that husband and dealer...
A brash Australian called Arthur turns up claiming to be Albert's long-lost elder son and, to Harold's horror, Albert believes him, agreeing that Wallaby Jim of the Islands as Harold calls the lazy, cadging interloper, should be his heir. Harold moves out into a shabby bed-sit and struggles to make a living with his hand-cart. Then his father visits and asks him to return. Arthur sold the horse and cart and disappeared. Eventually Harold agrees and, as they turn the corner, they see their horse and cart coming down the road.