In a play acted and written by the same person, it stands to reason that she will draw most of the focus: in this case, Phoebe Waller-Bridge has long been someone worth paying attention to, but has only recently come to the fore as one to watch closely. This self-penned monologue gives her much opportunity to waggle her witty, brusque and acerbic tongue, and even though there's nothing on stage bar her and a chair, there's never a slow moment.

The story seems, at first, the classic tale of a gen-Y, self-employed, downwardly mobile, sexually voracious, often drunk 20/30-something in desperate need of anything to halt the decline. Waller-Bridge's Fleabag is trying to balance any number of scales: an overactive sex drive and a serious dependable boyfriend, a failing cafe and money by various means, disdain and fear, family and work, feminist and... all of the classics really, and stories countless hours of Sex and the City and Girls (at the upper end of that spectrum) have been devoted to.

But behind that facade, just as in those two examples, lingers a collection of rather real issues, mostly collected around the impossible-to-answer question of what femininity is and how to be a modern woman. In Fleabag's case, this is also tied up with trying to be responsible and an adult, as well as facing up to your own failings – and each strand is given plenty of room to breathe in a play that focuses on the funny side of these questions whilst still not being afraid to ask them.

The plot seems to ramble at certain points, but it's just part of the charm: this feels less like a "story" than a description of a day-in-the-life: a character snapshot, which Waller-Bridge delivers with such truthful humanity that it's hard not to imagine personal similarities. She owns the small stage at the Soho, despite her lack of movement, props and set, and despite the character's taciturn nature, we develop a detailed imaginary portrait of what's happening to her.

And it's funny. My goodness, it's funny – without resorting to the idle cliches of the genre. We're not subjected to endless punning on partners' sexual proclivities or banal one-liners – every joke feels real, natural and part of the character, with even the most bizarre situations finding a relevance and feeling grounded in the story. Most of the humour borders on the black, and it's not short on sex gags, but the interplay between the story and the jokes feels just right and rarely exploitative.

The final twist(s) aren't too riveting, but they do put a nice coda on the end of a piece that might otherwise have fizzled out a little – and move the piece away from being too much like a stand-up gig, which it occasionally feels like it's veering into. But it's hard to find fault otherwise: this is really rather brilliant, and absolutely lives up to the hype it built up in Edinburgh. Not one to miss!

Fleabag, at Soho TheatreChris Hislop reviews Fleabag at the Soho Theatre.5