Entertaining Mr. Sloane opens with a frumpy, middle-aged woman named Kath showing her modest home to a potential lodger, a street-smart and rough-around-the-edges twenty-year-old named Sloane, whom she met earlier that day at the public library. Kath quickly suggests to Sloane that she is open to a sexual relationship and discloses that she once had a child out of wedlock, whom she gave up for adoption. Sloane decides to rent a room, sharing that he grew up in an orphanage.

Kath's elderly father, Kemp, enters and initially mistakes Sloane for his son, Ed. While Kath is in the kitchen, Kemp converses with Sloane and toasts crumpets (small cakes) over the electric logs in the fireplace. Kemp soon realizes that Sloane resembles the young hitchhiker who, two years prior, murdered Kemp's former employer. Kemp then stabs Sloane in the leg with the toasting fork. Kath returns from the kitchen, reprimands her father for his uncouth behavior, and tends to Sloane's injury, insisting he remove his trousers so she can apply antiseptic and a bandage. While attending to Sloane's wound, Kath ignores the doorbell, anticipating a nosy acquaintance who might gossip. She coyly attempts to seduce Sloane and sends him upstairs for a bath. Kath demands an explanation from her father and eventually sends him to Sloane's previous lodging to collect his belongings.

Kath's brother, Ed, then appears. Involved in a vague "business" with apparent underworld ties, Ed has come to get Kemp's signature on papers to commit him to a retirement home. Ed doesn't reside with Kath and their father, but overheard the conversation about the new tenant and now forbids Kath from taking in Sloane. Ed already suspects a potential sexual relationship between Kath and the new lodger, asserting that rumors of such behavior could damage his reputation and career.

Ed insists on meeting Sloane. Upon doing so, Ed is immediately drawn to Sloane himself. The homosexual Ed dismisses Kath, interviews Sloane, and offers him a job as his personal chauffeur. As Sloane goes to eat, Ed informs Kath that he will cover Sloane's rent. Ed departs, leaving Kath alone with Sloane, who has returned from the kitchen. Kath quickly seduces the willing Sloane on the living room sofa as the first act concludes.

One morning, six months later, Kath returns from a shopping trip to find Sloane lounging on the sofa, dressed in boots, leather trousers, and a white T-shirt. Sloane tells her that he is resting while Eddie repairs the car, as he is nursing a hangover from a late night out with three male friends. As Kath questions him about women, Sloane accuses her of being jealous and trying to control his life, warning that he will leave if she continues.

Kemp enters, searching for his pills, but declines Sloane's offer to help locate them. While Kemp rambles, Kath discreetly informs Sloane that she is pregnant. After Kemp departs, Sloane refuses to marry her but, to appease Kath, he gives her a locket his mother had given him as a gesture of respect.

Ed enters and competes with Kath for Sloane's attention. After Sloane goes to the kitchen, Ed hints that he might fire Sloane from his chauffeur job due to joy-riding the night before. Kath insists she needs her "baby" because Ed took away her other child, whom she had out of wedlock with Tommy, one of Ed's former friends. When Sloane returns, Ed traps him into admitting he was with a woman the previous night and advises him about the unreliability of women. Sloane agrees to move out and stay with Ed once he receives...