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The movie, which cost less than £3 million to make, helped make a huge star out of Madonna a year after she released her first single, Holiday.
She wore her own clothes for the part and the skirts over leggings, lacy gloves, rubber bracelets, giant hair bows and sunglasses, became huge in the Eighties.
Mark Rubinstein, one of the producers of the musical, said: "It's going to be all Blondie songs.
"It sets the world before Madonna, when there was Debbie Harry and Blondie. She's from that world and that time. Moment of Truth (the new song) is different."
Susan Gallin, the originating producer, said: "It will be very close to the movie.
"The story is universal. It's a quirky, off-beat movie about women who change their lives and end up with the lives that they were meant to have.
"I asked Debbie if I could send her the treatment, that was a Friday, and by Monday she called and said 'it's great, I love it. Let's do it'. She just loved the idea.
"We're so excited about doing the show in London. It feels as though Blondie and Debbie Harry were embraced here first.
"It just feels right that a musical with her music should happen in London first."
She added: "We would like to have Madonna come to see the opening night. It was her break-out movie. She was wonderful in it. Interesting, quirky and fabulous."
Williams, 24, playing Susan, said: "I didn't see the film when it came out. I was too young. I only saw it at our first workshop."
She said Susan would be a "cross between Madonna and Debbie Harry," with influences from Courtney Love, adding of Harry: "She's the epitome of cool. She's timeless and effortless."
She added: "Susan is drawn on so many different people. But she's Susan, she's not Debbie, not Madonna and not Courtney Love.
"It's about not having to conform to other people's ideas. Everyone sometimes feels like a fish out of water. Everyone can relate to it. It's female empowerment.
"For the generation that don't know the film it will give it a whole new lease of life."
Price, 25, from Wigan but now living in London, steps into the shoes of Rosanna Arquette, who won a Bafta for the movie role.
She said: "I've only seen the film once, before the audition last year, and I probably won't see it again because I don't want to copy it. They want us to bring ourselves to the parts."
She added: "All the fashion from Desperately Seeking Susan is just coming back. I don't know what Roberta will end up wearing. It could be anything."
The musical is written and conceived by US writer, director and actor Peter Michael Marino, whose other writing projects include Hollywood Nurses, an homage to lesbian pulp novels of the 1950s.
The production will open at London's Novello Theatre on October 12.
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