The photographs were discovered recently by a member of the film crew, who mailed them to Miles at her Manhattan home. John Clancy, the Obie award-winning director of Tim Fountain's new stage version of Midnight Cowboy, which has its world premiere in Edinburgh, is studying the images, making mental notes for the design of the show.
"Obviously, we're not doing a play based on the movie," says Clancy, 42, who is also an actor, writer and serial Fringe First winner for productions such as Horse Country, Fatboy and last year's Screwmachine/eyecandy. "The film and the novel are two incredibly deep wells we're pooling. And this is a wonderful resource for our production, because these images capture the 1960s - the era in which the play is set - perfectly."
However, it is Miles's private memories of the 1969 classic that are invaluable to Clancy. The 73-year-old, New York-born-and-bred veteran of 49 movies and numerous stage roles, has agreed to share her behind-the-scenes stories over lunch in New York.
Miles is a fund of information about the making of the movie which won Oscars for best picture, best director and best-adapted screenplay in 1970. It was, she points out, the first X-certificate film to be released by Hollywood. There were Academy Award nominations for best actor for the film's rising young stars - Dustin Hoffman and Jon Voight - and another for best supporting actress for Miles for a six-and-half-minute scene which made movie history; no-one had received recognition for such a brief film role before.
In Midnight Cowboy, Miles plays high-class hooker Cass Trehune, a role that will be recreated by Emma Kennedy on stage. The film was directed by British director John Schlesinger and written by an American, Waldo Salt. In a neat twist, the new play is being directed by Clancy, an American, and written by a British playwright, Tim Fountain.
Fountain is the author of the 2004 Fringe hit show, Julie Burchill Is Away, and Resident Alien, about the late Quentin Crisp. Crisp became a close friend of Miles when he moved to New York and she knows Fountain. They met in Edinburgh when she brought her one-woman show, It's Me Sylvia - Live & On Film, to the Fringe in 2000. She is convinced Fountain's stage version would benefit from a narrator, a role for which she's prepared to volunteer. "Hey, I'm an actress, I'm always hustling for the next job," growls Miles, who appeared in Sex and the City. "If only we could afford you," Clancy tells her. "It's a brilliant idea." Nevertheless, some terrific and less costly ideas emerge over the hamburgers and fries.
First, though, Clancy wants to finish examining Miles's photographic collection, which includes striking images of Jon Voight as Joe Buck, the eponymous cowboy, strutting down Times Square.
A dishwasher from Texas, Buck goes to New York dressed as a cowboy to fulfil his fantasy of living off rich women. Instead, he meets up with Ratso Rizzo (Dustin Hoffman), a crippled consumptive guttersnipe - and the touching, emotional relationship between these two lonely people is the heart of the story. "But it's not a gay love story, like Brokeback Mountain," insists Clancy. "It's just a beautiful love story."
In Edinburgh, Joe is played by newcomer Charles Aitken and Ratso by Olivier award winner, Con O'Neil. Their chemistry, according to Clancy, is as explosive as that between Voight and Hoffman. "I just hope those guys have a certain energy, a New York energy," Miles says, recalling that the movie and the novel offer a spellbinding glimpse of life in New York "and the way we lived then".
Gazing at photographs of herself with Voight, Miles says: "We rehearsed our scene alone for ten days. Jon would come to my apartment on Central Park South dressed in cowboy hat, jeans and boots. My neighbours thought I had this cowboy toyboy. If only! We came up with many of our own ideas for the scene, including the TV remote crushed beneath us on the bed, as we 'have sex' and the TV zaps from programme to programme. John Schlesinger wanted us to make our own imaginative contributions. He loved it if you came in with interesting ideas. I know he worked in this free way with Dustin and Jon for all their scenes, too."
"I've done lots of research, but had no idea this was how Schlesinger worked," Clancy tells Miles, who reveals that, originally, her scene with Voight was 30 minutes long. "It's far too long! I told Schlesinger. He said, 'OK, Sylvia, go home and rewrite it'. I did; I cut it to six-and-half-minutes. We filmed both versions. I had no idea until I went to the opening night at the Coronet Theater, on Third Avenue, which one he'd used. When the film finished, there was a ten-minute standing ovation."
Talking to Miles about how the actors were so heavily involved in the rehearsal process changed the way Clancy approached the stage version. "We're allowing the actors to adapt and make the roles their own. It's been a very collaborative approach, thanks to Sylvia telling us this. I've used this method to rehearse the scene, for example, in which my wife, Nancy Walsh, plays Shirley, a socialite, who invites Joe to a drugged-out party."
On screen Shirley is played by Brenda Vaccaro, wearing only a fox fur coat. "Of course, Andy Warhol should have been in that scene," reveals Miles, adding that many of his Factory "superstars", such as Viva and Ultra Violet, do appear, although Warhol had been shot by Valerie Solanis shortly beforehand. "On June 3, 1968, I was at the Actors' Studio waiting to meet John Schlesinger, when this kook arrived asking for Andy. I told her he wasn't there and shut the door because she looked so crazy! It was Valerie, who immediately went round to Andy's house and shot him. I'll never forget that day - at 4am I got the call to say I'd got the role of Cass."
Stories such as this are gold-dust to Clancy, who says: "It gives me a thrilling sense of the historical perspective. Talking with Sylvia is better than watching the movie or listening to that famous score."
The soundtrack is by John Barry and the theme song, Everybody's Talkin', sung by Harry Nillson, haunts the film. "The music was to have been written by Bob Dylan," Miles discloses. " I don't know why, but he ended up not doing it. However, he loved my scene so much he wrote Lay, Lady, Lay for me. You know how it goes?" she asks Clancy. And they duet: "Lay across my big brass bed..."
Then Miles produces a picture of herself and Voight on the bed. "The result was Bobby - honey, he'll always be Bobby Zimmerman to me! - and I had an affair for 26 years, because he fell for me in Midnight Cowboy."
After listening to this story, Clancy discovered the musical leitmotif for his production. "Sylvia's saying that tipped it for me. I kept hearing Dylan. Now, almost every scene transition is underscored by a Dylan song."
As Clancy tells Miles, no-one who has seen the film forgets the moment her character teeters into the frame, wearing a tight mini-dress and killer heels, with a poodle on a leash. Later, in her Park Avenue apartment, Cass screeches postcoitally at Joe, after he reveals he planned to ask her to pay him for the fast and furious sex they have indulged in.
Will Miles repeat those words for us today? "Sure, I wrote them," she responds, with a throaty laugh. "Who the hell do you think you're dealing with? Some old slut from 42nd Street? In case you haven't noticed, I'm one hell of a gorgeous chick - and I'm 28 years old." Then she winks broadly.
"Oh man, what a privilege!" exclaims the director, kissing the lady's hand. "Sylvia Miles, a legend in her own lifetime."
• Midnight Cowboy is at the Assembly Rooms until 28 August