PHOEBE Waller-Bridge is a busy woman. The thirty-two year old actress who burst onto our TV screens as writer and star of Fleabag, the tragi-comic sort of sit-com about a supposedly independent woman on the verge is currently overseeing Killing Eve, her new TV drama which she's written for BBC America. As an actress, Waller-Bridge is also filming a big screen project which we can't talk about, but which has already been outed as being part of the ongoing Star Wars franchise.

These are both pretty good reasons why Waller-Bridge won't be appearing in the brief Edinburgh Festival Fringe revival of the original stage play of Fleabag, when it opens next week at the Underbelly, where it was first unleashed to the world in 2013. In her place, Maddie Rice will take on the role of the potty-mouthed anti-heroine after touring Vickie Jones' production for Waller-Bridge and Jones' DryWrite company in association with Soho Theatre. This doesn't mean Waller-Bridge has turned her back on what turned out to be her calling card now she's hit the big time. Far from it.

"I'm so pleased it's in the safe and wonderful hands of Maddie," says Waller-Bridge. "It's because of Edinburgh we found Maddie as well. We initially thought we were looking for a really dramatic actress who could do all the dark stuff, when actually it's about getting someone who can be funny. But Maddie's really made it her own. She's a different Fleabag, but still has the same heart, and I feel really excited about people seeing where it started."

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Fleabag's roots actually go back a bit further, to a spoken word night Waller-Bridge was persuaded to take part in.

"I had done a little bit of writing," she says, "and a friend asked me to do a ten minute storytelling slot at this stand-up thing. I was really nervous, but but I thought I'll never get a chance to do this again, and that was a really cathartic moment that made me put my writing where my mouth was, and this character started falling out of me that was very personal to my and my friends.

"Then when I did it at the spoken-word night, the audience got really behind it, and this woman who'd had a few glasses of wine said I should take it to Edinburgh. A producer who was there overheard hat, and the next day she rang up and said, I've got you a slot, and the ten minutes I did at the spoken-word night ended up being the first ten minutes of the play."

Waller-Bridge says the stage version of Fleabag was "probably the biggest challenge of my writing and acting life so far. Because it wasn't something I'd planned to do, or was particularly yearning to do, I was blindly writing this fifty minutes of material, filling it with gag after gag so you'd never get bored. I wanted it to be furious and truthful, and something that spoke to me, and if it bombed then it bombed. A lot of people talk about how raw it is, and I think that's where it came from. It was a free pass to do something wild."

With Fleabag commissioned as a TV pilot shortly afterwards, Waller-Bridge was able to expand on the play's ideas beyond a solo show in a way that has now come to define one of the most fearlessly upfront depictions of young women today. It also meant that another script in the TV slush pile, Crashing, was picked up, filmed and broadcast in a way that set the liberated tone of Waller-Bridge's writing style. It was the dark humour of Fleabag, however, that tapped into something that seemed very now.

"When you see someone like Fleabag trying so hard, you're with them," Waller-Bridge speculates on Fleabag's appeal, "and then when the mask slips and you see how much pain she's in, there's something about humanity that gets you. Even if it doesn't relate to your own life, I thin you can still feel it. It's a rare thing to create a character who people connect with, and who I get to play myself."

A second series of Fleabag seems likely, though one has yet to be confirmed. In the meantime, Waller-Bridge has Killing Eve – "an eight part drama about female assassins" – and the film we can't talk about to be getting on with.

"Having to let go of Fleabag for a few months is a good thing," she says, "but I can't wait to get back to her. I'm already starting to miss her."

Fleabag, Underbelly, August 21-27, 5.15pm www.underbellyedinburgh.co.uk