Best known for her vagina bodysuits and sexually charged lyrics, Peaches seems an unlikely art-world darling. But in 2007, the French artist Sophie Calle asked the electropunk queen to respond, in the form of a song, to a breakup email Calle had received. The work was one of 100 that appeared in Calle’s show Take Care of Yourself, which premiered at the Venice Biennale. Then in 2013, Yoko Ono invited Peaches to re-enact her seminal 1964 performance Cut Piece, letting audience members snip away at the singer’s clothes until they had entirely gone. Now, 20 years after unleashing her sex-positive signature song Fuck the Pain Away, Peaches finally has an exhibition of her own.

“I was like, ‘I want to make new art,’” the Berlin-based, Canadian musician says of the show, which is titled Whose Jizz Is This? A nod to her 2015 track Dick in the Air, it’s a “deconstructed musical in 14 scenes”, revolving around a series of new works featuring sculpture, prints, video and an eclectic cast of sex toys. This comes to life via a carefully choreographed light show and soundtrack. The exhibition coincides with an over-the-top live show, There’s Only One Peach with the Hole in the Middle, involving 40 performers and musicians. Having just opened at the Hamburg’s Kampnagel theatre, it will play for one night only at the Royal Festival Hall in London later this month.

A speculative, post-human tale with an absurdist twist, the exhibition chronicles the emancipation of the “fleshies” – a community of double-ended silicone masturbators that have broken free from human domination and are now seeking their own sexual liberation. “They look like disembodied objects where all you’re thinking about is holes,” says Peaches of the male self-pleasuring devices, which she accidentally encountered in a crudely made YouTube review video. This also appears in the show. “I thought, ‘What if the fleshies decided to rewrite their own narrative and realise they have all the equipment to satisfy themselves in a sexual way?’”

‘I wanted to make new art’ … Peaches. Photograph: © Peaches, 2019

It’s a storyline that touches on a lot of topical issues. “These objects have been jizzed into, that’s what they’re used for,” says Peaches, linking this to the theme of consent. It’s something she inverts in one of the show’s key pieces: a 7x9m fountain made of four large fleshies squirting liquids into one another. “It’s consensual,” she says, “because it’s between them.” She calls it “quite disturbing, quite deep, if you think of all the elements involved – but a lot of fun too”.

From artist Portia Munson’s childlike pink dildo installations to Laurie Simmons’ introspective photographs of life-size love dolls, the sex toy (formerly known as “a marital aid”) isn’t new to galleries. But Peaches’ references are far more crass than that, as evidenced by her raunchy stage aesthetic and often grotesque props. However, her multi-boob neck pieces aren’t too dissimilar from Sarah Lucas’s sculptures with tights, and her crowd-surfing inflatable condom is worthy of the filthiest Paul McCarthy installation. These are two contemporary artists she admits to having conversations with “in my mind”.

Art wasn’t always present in the singer’s life. “I grew up in a Jewish community where you listened to Fiddler on the Roof and West Side Story,” says the woman born Merrill Beth Nisker. These musicals could explain her early penchant for the theatrical, not to mention her one-woman remake of Jesus Christ Superstar and body-positive opera rock film Peaches Does Herself. Peaches, now 52, was a late bloomer as a musician. After teaching drama to young children at a YMCA and private schools for nearly a decade, she came of age among Toronto’s fine indie scene, performing with Jason Beck (aka Chilly Gonzales) and Leslie Feist, with whom she shared an apartment above a co-operative sex store in the late 1990s.

Does she think the mainstreaming of queer culture has revived interest in her work? “Maybe I’m naive,” she says, “but I feel like the interest never went away.” Instead, the feminist icon – who counts Iggy Pop, Christina Aguilera and Pink as collaborators – prefers to think about how the changing landscape has made her reconsider her oeuvre.

Complex messiah … performing Peaches Christ Superstar in New York. Photograph: WENN Rights Ltd/Alamy Stock Photo

On stage, she has been experimenting with new lyrics, introducing more inclusive terminology to previously gendered songs. “I don’t have to make the choice, I like girls and I like boys” has become “Gender fluid make some noise”. And she has recently been collaborating with such younger performers as the New York “drag terrorist” Christeene and the Australian aerial burlesque artist Empress Stah. “In a way, I learn,” she says. “Things move, things grow, things change.”

These’s nothing new about a musician trying to cross over into the gallery. Godmother of punk Patti Smith has wandered in and out of art circles throughout her career, showing her quiet black-and-white photographs everywhere from Paris to San Francisco. Meanwhile, Björk may still be recovering from her badly received retrospective at MoMA PS1 in New York four years ago. While it is too early to assess the impact of Peaches’ flamboyant fleshies, they certainly reflect a key aspect of their creator: radical queer joy.