The first few Carry On films are largely variations on a theme, with well-meaning bumblers wreaking havoc in a variety of jobs. Carry on Cabby keeps the work based setting, but cuts back on the bumbling to concentrate on the battle of the sexes.
Charlie Hawkins (Sid James) runs a highly successful cab firm, and the cab firm runs his life, much to the chagrin of his neglected other half Peggy (Hattie Jacques). To teach Charlie a lesson, Peggy clandestinely starts her own business, Glamcabs, employing only sexy young women as drivers. As Glamcabs starts to poach Charlie's business, he resorts to sabotage.
This may look like a case of women getting the upper hand, but, of course, this is a Carry On film, so for the women to fight back they have to use sexist methods, and the drivers are picked purely on their looks and legs.
The script is more story driven than later films in the series, favouring a tone that is warm and innocent rather than the knowing smut that would follow. There is a focus on relationships, and subtle little characterisations, such as Charlie helping out ex-army people, a code he sticks to loyally even if it means employing a hopelessly clumsy halfwit like Pintpot (Charles Hawtrey)
The end result is a film played straight and realistically by an excellent cast, and one more grounded in reality, and less cartoonish than the series would become.