Stanley Kubrick was one of the greatest, and often demanding, film directors of all time, making movies from Spartacus to Full Metal Jacket. And if it had not been for his friend Steven Spielberg, there may also have been one called Aryan Papers, set in the Nazi-occupied Warsaw Ghetto.

The story of the movie Kubrick never made – despite investing enormous energy into it – is to be told through a new art installation at the British Film Institute in London by the Turner-prize nominated artists Jane and Louise Wilson.

The twin sisters were invited to delve into the Stanley Kubrick archives at the University of the Arts in London and come up with a piece of work to coincide with a major Kubrick season on the South Bank this year. What they alighted on was the fascinating story of Aryan Papers, a film that he was adapting from Louis Begley's 1991 novel, Wartime Lies. It tells the story of a young Jewish boy hidden as a Catholic by his aunt.

The Wilsons had a wonderful time in the archives. "We did feel a bit like kids in a sweetshop and there is so much there you could easily spend days in there, it really is incredible," said Louise. "Of course the films he has made are so well known we wanted to concentrate on something he hadn't done."

Kubrick, a secretive obsessional perfectionist by any standards, spent months on preproduction for Aryan Papers, even casting the Dutch actor Johanna ter Steege in the lead role. The Wilsons came across intriguing stills of Ter Steege in different costumes, shot at different angles and in different lights and, taking these as a starting point, then approached the actor herself. The resulting film will cut between the stills and their interview with Ter Steege.

"It is a sort of bittersweet story," said Louise. "The film would have been a major thing to happen for her, or for anyone. It was memorable for her to meet [Kubrick] and work with him, she had to keep the whole thing quiet for eight months. It was obviously a tremendous blow that the film never happened. She had never had that kind of rigour from a director."

Kubrick put an awful lot of effort into Aryan Papers: writing the screenplay, casting Ter Steege and travelling to the Czech town of Brno as a possible location for wartime Warsaw. That the film was never made seems to be due to a combination of factors. Spielberg's Schindler's List came out in 1993 and Kubrick may have felt beaten to the line. He may also have got sidetracked by his project to make the film AI – which Spielberg ended up making after Kubrick's death.

Or the whole project may have been too much for him. Louise said: "Having spoken to Johanna, it sounds like he got very depressed. He was so immersed in this research I think he found the process quite disturbing and upsetting."

• Jane and Louise Wilson's installation will be at the BFI Southbank, London, from 13 February to 19 April.