Ayşe Deniz Gökçin is telling me about a restless moment she had in a Turkish cinema in 1987. Her mother, Ayşegül, had gone to see Amadeus, the sumptuous, multi-award-winning film about the rivalry between Mozart and Salieri. Tiny AyşeDeniz had a destiny as a classical pianist, so the music may have made an impression on her. She might have enjoyed watching the movie too, if she could have seen it. But she was still in the womb of her mother, who was seven months pregnant with her.

“Apparently I wouldn’t stay still,” laughs Gökçin. “So she decided there and then that I was going to be a classical musician.”

There may have been another clue in that child’s restlessness: this would not be any old classical musician, but one who might shake things up and push a few boundaries.

Confirmation of her mother’s cinema hunch came soon enough, when the baby girl took to the piano like a flamingo to the Sultan Marshes. “We had an upright piano at home in Ankara,” she recalls, “and no one knew how to play it. But when I was two, my parents would put me by it and I would improvise and sing for hours. My dad had a video camera and he recorded me. It was more like an impression of a pianist than real piano-playing; I would even turn the pages of the score as I played.” By the age of six Gökçin was a serious piano student, and her strict Turkish teachers had her playing in front of her first audience. She managed a note-perfect performance of a charming Beethoven écossaise, despite running a fever.

“I love going on stage,” she tells me, her brown eyes seeming to flash with excitement. “It always felt very natural. I would perform better than at any other time. It helps me concentrate. Okay, it sounds egotistical, but I like being in the spotlight,” she laughs. “I like it when people are finally there to listen to me after all that hard work. Otherwise, there’s no point: I don’t want to do music just for myself.”

And there have been years of hard work. Gökçin, now 25, reels out the story of her education: how she went from one teacher to another as she gradually grew more and more proficient, and how her enterprising father, Balamber, contacted Rosalyn Tureck, the Chicago-born pianist, harpsichordist and interpreter of Bach, having spotted her name on a CD of 20th-century pianists and fancied that Tureck sounded like a Turkish name. “He emailed her manager, saying his daughter played the piano, and sent a recording of a Bach performance I’d done. She got back to him, saying she wanted me to come to Oxford to take lessons with her. But then she said she had decided to move to Marbella, for health reasons, and that I should go there to study with her.”

It was an irresistible offer, but relocating to Spain to study with this 86-year-old woman proved a wrench for the 12-year-old prodigy. “I was just a kid, and I was homesick. My mum came with me, but my dad had work in Turkey, so he had to stay. And culturally, I was lost. Marbella’s not a cultural place: it’s a tourist resort. I went to a British school, and it was full of these rich kids. When my mother dropped me off in the morning, they thought she was my servant!”

Gökçin returned to Turkey, then faced another succession of teachers and periods of upheaval, including training at a music college in New York State. In 2011, the bicentenary of Franz Liszt’s birth, inspiration struck. “I was reading about how he created the image of the pianist as a big star, and played to thousands of people. The more I read, the more I thought, ‘He was a rock star!’”

Then she started finding parallels between Liszt and one of her favourite rock bands, Pink Floyd. “Liszt was interested in the idea of the romantic hero who isolates himself from the rest of the world, and the main character in Pink Floyd’s The Wall, of course, creates this wall around himself.”

Shortly after arriving in London to study at the Royal Academy of Music, she was tinkering with some piano arrangements that fused Liszt’s Dante Sonata with Pink Floyd’s 1979 hit ‘Another Brick in the Wall’. She took the risk of bringing the project to a lesson, showing it to the head of the academy’s keyboard department. “I thought he would be strict and conservative, and say, ‘What are you doing? How dare you bring this commercial thing to my class?’ But he thought it was very interesting. I was so happy.” Enjoying herself, she moved on to two more Floyd songs, ‘Wish You Were Here’ and ‘Hey You’, ending up with a three-movement fantasia.

Shortly after graduating with a master’s, AyşeDeniz Gökçin found herself in her favourite place – the spotlight – after she released an EP, Pink Floyd Lisztified, and brought her new music to the concert hall. At a London concert in St James’s Church in Piccadilly, I watched as Gökçin played her fantasia, caressing and attacking the ivories before an enraptured audience. There were frequent murmurs of recognition as those well-loved rock tunes emerged from cascades of luscious Lisztiness. The concert’s location was perfect not only for its heavenly acoustics: it was also just yards up Piccadilly from No 201, where Pink Floyd themselves recorded a session for the BBC in 1968.

The band’s music has been covered extensively, notably by a series of tribute bands (groups who re-create the music of the original musicians in perfect detail). I remember in 1997 watching a convincing performance in Bromley by an outfit calling themselves Pink Fraud. But Gökçin’s blend of their music and Liszt’s was much more creative and inspired. By coincidence, shortly before I met her I had interviewed Nick Mason, long-serving drummer with Pink Floyd, so I asked his opinion of her music. He said he loved her version of ‘Wish You Were Here’. “But then I would always choose a reinterpretation over a slavish copy,” he remarked. “What’s the point of re-creating every dropped drumstick?”

Gökçin has had other nice remarks from fans of both classical and rock music, and there has been some cross-genre conversion. “People have said, ‘I never knew about Liszt.’” During a pause in our interview, she chuckles at her smartphone as she finds messages from her fans on Facebook – from Denmark to Dubai – saying how much they love her music, and suggesting other Floyd songs she could rearrange. At the end of November she releases an album, Pink Floyd Classical Concept.

While she is certainly experimental, there is something of the instrumental purist about her too. Asked if she has ever been tempted to use electronic keyboards, she replies: “No way. I’m an acoustic-piano person. I want to create all the different sounds with the piano. My aim is to develop its potential.”

Isn’t there a danger, I ask, of becoming stereotyped as “the girl who classicises Pink Floyd”? “No!” she replies emphatically, before dropping hints about some of her latest projects. She has created an all-piano version of Michael Jackson’s ‘Billie Jean’. Released as a download and well worth watching on YouTube, her virtuoso performance is jaw-dropping. It would have made Liszt dance his socks off.