The first time we get a proper look at the star of Agent Carter, she is pushing her way down a New York street through a sea of grey-suited men walking in the opposite direction. Her red hat and lipstick contrast with the masculine blankness all around. It is 1946: much as Peggy Carter might stand out to the viewer, in her own time – full of returning GIs and reasserted patriarchal structures – she is invisible.

Throughout the first series of Agent Carter (Sundays, 9pm), the first and so far only solo female-led property in the Marvel Cinematic Universe (MCU), this disjunction in perspective is exploited to great success. Despite her extraordinary service record in intelligence during the Second World War (seen in the first Captain America film, The First Avenger), in peacetime Peggy has been relegated to the role of secretary at her agency, fetching sandwiches and filing for her male colleagues. The investigating, baddie-slaying and world-saving that she does in her spare time is, by and large, for viewers’ eyes only.

Although completely integrated into the MCU, the judicious use of flashbacks and light-touch exposition make it entirely possible to come to Agent Carter with only the vaguest idea of the backstory and yet still revel in its witty script and wry depictions of 1940s workplace sexism. At only eight episodes, the show feels tightly plotted.

Hayley Atwell has already played Peggy in a handful of Marvel films, and it was undoubtedly her presence and gravitas on the big screen that finally convinced executives that a non-superhero female character could star in their own story. In Agent Carter, she is remarkably contained, her anger at the injustice of her situation and grief about what has happened during the war surfacing only as grim determination. She suits the period setting very well, prompting comparisons from some critics with Lauren Bacall. There is certainly something of “the look” about her – that sultry expression synonymous with film noir and female dissatisfaction.

Perhaps surprisingly for a show as all-American as this, Atwell spearheads a trio of British lead actors. A superbly moustachioed Dominic Cooper joins her as the inventor Howard Stark (father of Tony, aka Iron Man) and James D’Arcy is Stark’s butler, Jarvis. These two are crucial to the plot arc: Stark appeals to Peggy for aid after he is accused of treason when some of his military tech gets stolen. Under the noses of her colleagues, too busy making sexist remarks about her “women’s troubles” to notice, Peggy gets on the trail of a shadowy organisation called Leviathan and uncovers a Russian plot to destroy New York.

D’Arcy’s Jarvis provides welcome comic relief from Peggy’s single-minded pursuit of the bad guys – his tightly wound English butler is hardly an ideal spy’s sidekick. At one point he tells Peggy to call on him any time she needs assistance, except later than nine at night. When she raises an eyebrow, he explains that he and his wife follow a strict evening timetable of “seven o’clock sherry, eight o’clock Benny Goodman, nine o’clock bed”.

Of course, Agent Carter has its camp, comic-book elements. How could it not? The Russian villain with the power to hypnotise strong men to do his bidding, the icily beautiful sleeper agent turned assassin and the henchman without a larynx who communicates only through a ghostly self-typing typewriter all provide the perfect foils to Carter’s derring-do. The clever use of a Captain America radio-show-within-the-show helps the viewer distinguish between the real peril Peggy is facing and the patriotic propaganda put about, at least to start with, by her colleagues. Sadly, the latter remain somewhat underdeveloped. You feel as if Carter, and Atwell, could have stood up to a more nuanced ensemble.

Above all, though, Peggy Carter is a woman you want on your side. When her roommate chastises her early on for her workaholic habits, saying, “There’s a difference between being an independent woman and a spinster,” we all wish we had Peggy’s confidence in replying, “Is it the shoes?” while slipping a pistol into her handbag. You don’t need super powers to come out on top.

Now listen to Caroline discussing Agent Carter on SRSLY, the pop culture podcast from the New Statesman.