Success has been double-edged for Isobel Waller-Bridge. After working for years as a composer for stage and screen, she saw her profile rise in 2016 when she worked on her sister Phoebe’s breakthrough hit, Fleabag. That was — and remains — the only time she has provided the music for something Phoebe has written and includes the mix of choir, brass and crunchy guitars that she added to Fleabag’s second series last year.

She has done other distinctive work since, not least the soundtrack for this year’s film version of Jane Austen’s Emma. We meet, pre-lockdown, in her agent’s office in a former hat factory in north London. She is publicity-shy, but keen to do her bit to help the shows she works on: in this instance the new production by the Royal Shakespeare Company (RSC) of The Winter’s Tale, which is due to be on in Stratford-upon-Avon this year. She has worked before with its director, Erica Whyman; she likes working with people who knew her when the name Waller-Bridge was not yet world-famous.

Waller-Bridge, 35, insists she is more introverted than her famous sibling. However, she shares Phoebe’s dynamite diction, some of her features, some of the conversational ability — so important to Fleabag — to make one feel almost instantly like a confidant. She won’t deny the impact of having worked on a series that, with its tragicomic, sexually frank look at a young singleton in London, broke through in a way that only a handful of shows do. She is a fan of Fleabag, she says, as well as having worked on it since it began life as a monologue at the Edinburgh Fringe in 2013. She also hates the idea that people might think she is piggybacking on her sister’s success.

She likes working with people who knew her when the name Waller-Bridge was not yet world-famous.

“Oh, I’m so sensitive to that. That’s horrifying to me. That sort of makes me want to hide and stop. I’m quite an introverted person and the visibility that came with Fleabag made me feel sunburnt for a while. I had to learn to navigate suddenly being attached to one piece of work when I felt so proud of all the other stuff. It was a phenomenon, it was kind of wild. I’m really proud of it. It’s complicated, my feelings about that, but … mainly positive.”

Any awkwardness she may feel in addressing the vexed issue of fame and glory, and reflected fame and glory, vanishes when she talks about her work. Music, she says with a laugh, “is my first language, more so than words”. Her credits are impressive. Television work in the past two years includes the John Malkovich Poirot thriller The ABC Murders, an episode of Charlie Brooker’s series Black Mirror and ITV’s adaptation of Vanity Fair. She has been writing for stage shows for most of the past decade; her credits include other work for the RSC, the Old Vic’s production of Woyzeck starring John Boyega, and Matthew Perry’s play The End of Longing in the West End in 2016.

That sense that one gets in conversation that Waller-Bridge is really listening to you, Whyman says, is what makes her so good at her job. “You are asking a theatre composer to hold the mood and world of a play,” she says. Watch Fleabag again, she suggests, and see how the music fuses the sacred with the profane to help us to fall in love with Andrew Scott’s “hot priest” character. “I think her contribution is really underestimated.”

Side by side: with her little sister, Phoebe, at this year’s Critics’ Choice Awards, in January.

Joe Murphy, the director of Woyzeck, says he asks Waller-Bridge’s opinion on every aspect of his shows, even the ones she’s not working on. He thinks her key contribution as a composer is getting the audience into the emotional inner life of the character. “I don’t think anyone does it better. Her understanding of people is amazing.”

She has been interested in music since the age of four, when her parents stuck her in front of a piano. She used to play duets with her mother, Teresa. Her father, Michael, she says, is “a brilliant guitarist” and used to be her roadie when she gave guitar recitals at school. She also plays the cello and wind instruments; not very well, she insists, but it all helps her as a composer. It was a creative household. “Mum always had this kind of open-door policy at home, so there were always people round.” Michael is a photographer who used to make fine-art holograms and he also set up a trading platform, Tradepoint, that functioned for a while as an online rival to the London Stock Exchange. “He’s a big inspiration, Dad.”

She also hates the idea that people might think she is piggybacking on her sister’s success.

The Waller-Bridge children are close in age: Phoebe is 15 months younger than Isobel. Their brother Jasper is two years younger than Phoebe. They remain best friends. “They are definitely my closest people, my siblings. I know I am really lucky to have both of them in my life,” Isobel says.

Phoebe was educated at an independent school, St Augustine’s Priory, near the family home in Ealing, west London, but Isobel went with a music scholarship to board at St George’s, Ascot, in Berkshire. She went to university in Edinburgh to study music, and studied for a master’s degree at King’s College London. At the same time she won a scholarship to do a diploma at the Royal Academy. Happier talking about musique concrète than she is about red carpets, she was planning to do a PhD before stage work came along. “The fact that I have any music career at all is amazing to me.”

She doesn’t come across like Fleabag’s uptight older sister, Claire. Indeed, she insists that no resemblance is intended. “Although there are a couple of things that happened in our lives that she put in there as funny moments …” Such as? “No, I’m not going to say! But no, I don’t really relate to Claire at all.”

Is she in a relationship? She’d rather not say. “I don’t mind talking about my family, but there is a limit.”

She understands the fascination with Fleabag — and, by extension, all things Waller-Bridge — while also wishing we would get past it. “With culture it’s really important for everything to keep moving, and when something occupies such a big space, that’s really wonderful, but there comes a time … I feel like Fleabag has saluted us and she’s gone on to do other things.”

Phoebe has gone on to write Killing Eve and co-write the new James Bond film, No Time to Die. The sisters will work together again. “But it’s got to be the right job,” Isobel says. “I have been asked to do things she works on and I have said no. Because they have to be the right thing for me creatively.”

Meanwhile, Emma was much talked about when it was released in February; people tended either to love this film by the American photographer-turned-director Autumn de Wilde or find it too upfront. “Yes, that’s the personality of it, it’s very direct, it’s not shy.”

Even before lockdown arrived, Waller-Bridge was planning to spend a chunk of time self-isolating, building a studio near her east London home for the album that Decca has signed her to record for its “post-classical” Mercury KX label. “I just get to be me. The album represents real privacy, which is important to me.”

She hopes to do live shows when the album comes out next year. “It’s lovely being a performer, but I would never be an actress.” Did she try? Briefly. She took a drama course when she was 18. She loved it, she says, “but knew immediately that acting was not for me”.

Among her fellow students was her sister. “And she took to it like a duck to water.” Was that galling? “No, that is what is so lovely about our relationship. We’re really opposites in so many ways. We have the same sense of humour, we see the world in a very similar way, but in terms of what we are like as people we are a very different temperature. Which I think is why our friendship really works.”