Shooting took place in New Mexico over the summer of 1975, known to Bowie fans as "the lost year" and which Bowie himself referred to as "singularly the darkest days of my life" and "so steeped in awfulness that recall is nigh on impossible - certainly painful".
He made his Hollywood debut at a time when he was supposedly taking such huge amounts of cocaine that he was suffering from paranoid delusions - something many suspect only added to the other-worldliness of his performance.
Bowie was living in an apartment in Los Angeles, having released Young Americans in March and declaring that "me and rock and roll have parted company", as well as announcing his intention of getting into the movie business.
However, as he said in a later interview, he also had other preoccupations: attempting to speak to the dead and using the power of his mind to change the channel on his TV. He had become obsessed by the occult and with the notion that witches were planning to attack him psychically, as was Led Zeppelin guitarist Jimmy Page. According to Angie Bowie, her husband exorcised their swimming pool because he thought he had seen the devil lurking at the bottom.
Living off milk, peppers and ice-cream, there were points, he claimed, when he weighed under six stone. Yet Clark believes he exaggerated his drug use to add to his mystique. "Look at the film," she tells me over the phone from her home in California. "Does that look like someone on heavy cocaine? No. His eyes are clear, his skin is clear, he is very relaxed. He had vowed to Nic Roeg that he would not do drugs while doing this film. I believe he kept his word. I think he made up all that other stuff just to be controversial, which he liked to do."
But Clark agrees that the late rock star was perfect for the role of a man from another planet. "He was so beautiful, just gorgeous to look at. In the film, he is at the height of handsomeness."
A new generation of fans can now see this for themselves. The Man Who Fell to Earth has been digitally restored and is being rereleased in cinemas and on DVD to mark the 40th anniversary of its UK release, and Clark is as enthusiastic about it now as when she first read the script. "I could talk about this film until I'm 90," she says. "I toot the horn of The Man Who Fell to Earth."
Bowie, she says, was a consummate professional who liked to rehearse until he was word perfect. "It turned out that he was really, really good. He loved the part. Any time we had a second to run lines for the next scene, we would sit and do back and forth back and forth, until we could get it really right. I attribute that to him being a musician. They are used to doing the same material over and over again at concerts."
The film quickly became notorious for its outrageous, often violent sex scenes, which required both actors to appear fully nude. Not that this came easily to either of them. "Those were my least favourite days of work," says Clark. "We had to do them because they were part of the script, but I could tell he didn't like doing it either. He was kind of rushing the scenes, like flinging me here, flinging me there. You can just tell when people are uptight about doing something."
Although he was friendly, Bowie stayed with his entourage at a large house away from the cast and crew's hotel. "We hung out a little bit but not a lot," says Clark.
After filming ended, in late summer, they didn't meet again until Christmas, by which time Bowie had recorded Station to Station, apparently using material originally intended for the soundtrack of The Man Who Fell to Earth.
"I was living in an apartment in Hollywood and I don't know how he found me, but there was a knock at the door and I opened it and there was David," she explains. "I could see his limo waiting for him. He said 'Merry Christmas' and handed me a little box. Inside was a brooch. He'd gone to the trouble of finding my address and buying me a gift."
When the film was released, reviews were mixed. The Daily Telegraph suggested that the arresting visual imagery contributed "more to our mystification than understanding", while the New Yorker's Pauline Kael hailed Bowie as "the most romantic figure in recent pictures, the modern version of the James Dean lost-boy myth".
Clark and Bowie met only once again, years later, bumping into each other on the street in New York, where Bowie then lived and Clark was doing a play.
She learnt of his death this January when she turned on her computer in the morning and read the headlines.
"I started wailing. I felt so guilty because I had known that his musical, Lazarus [a sequel to The Man Who Fell to Earth], was opening in New York and I thought, 'God, I should really show up for that. I should fly in and be there on opening night and surprise him'." But opening night came and went, and the reunion didn't happen.
In fact, Clark and Bowie almost met again on the set of David Lynch's new version of Twin Peaks. Bowie appeared in the Twin Peaks spin-off film Fire Walk With Me, as Agent Philip Jeffries, and was reportedly lined up to reprise his role in the reboot. "It's too bad we didn't get to work together again," Clark says. "That really would have been so great. But I'm glad the film we made together is getting a second chance. I just hope everyone loves it as much as I do."
