As usual, the legend is much neater than real life. Douglas certainly earned a reputation as a serial seducer, but he has consistently denied being treated for sex addiction; his problem was alcohol. At the time, he says, "Basic Instinct was in the air." But he wasn't Detective Nick Curran any more than he was any other characters. It has always distressed him when young guns from Wall Street recognise him as Gordon Gekko, numero uno master of the universe, and give him the thumbs up. "Gordon Gekko," he says, "was not a hero." He certainly doesn't want to be mistaken for him.

These days, Douglas is the sort of star who uses the subway to take his daughter to school. He has always been a vigorous advocate of nuclear disarmament and has taken up the cudgels for gun control. His assiduous courtship of young, glamorous Catherine Zeta-Jones has turned into a 13-year marriage and two children – Dylan, 12, and Carys, 10 – with that initial predatory foxiness lost in the cosy fug of domesticity.

He was 55 when he got married, he says, so more than ready to scale down his job to stay at home with the kids. "That has been my priority and what gave me real enjoyment," he says. When he talks about his wife during an entertaining interview at the Cannes Film Festival, it is to enthuse about her golf game. It was his dream when he started playing golf, he says, to find a woman who would hit the fairways with him. "You'd see these couples on the golf carts and at weekends they would go out and play golf together. When I first started with Catherine I said, 'Do you like golf?' And she said, 'Oh, I love golf'. I melted, man." It's hardly the sentiment of a dedicated Lothario.

But none of this matters. Any film star is at least partly a fictional figure. Douglas' own small genius in his Basic Instinct prime was his ability to play characters who were "morally indolent, compromised and greedy for illicit sensation", to quote critic David Thomson, while remaining likeable. Thus was his public image fixed. At the first screening of Fatal Attraction, he once recalled, the audience laughed when his character, Dan, came home after being out for the night and ruffled the marital bed to look as if he had slept in it. "The producer, Sherry Lansing, turned to me and said 'I can't believe it; they have forgiven you already. You are blessed with the gift of charm.' It made me wonder. What can I get away with? How far can I go?"

Here it is: how far Michael Douglas can go. In Behind the Candelabra – purported to be Steven Soderbergh's last film, which was made for American television – Douglas plays the aged but thoroughly nipped-and-tucked Liberace, the twinkle-fingered Las Vegas entertainer who mixed ermine, rhinestone and satin suits with rapid-fire Chopin. Liberace was as publicly camp as any man who ever lived, but his legions of largely female fans refused to notice. Every now and then, his agent would drop a suggestive story about a girlfriend while Lee, as he was known, remained in his fabulously stuffed closet.

In private, however, he was surrounded by young men. Behind the Candelabra is based on the autobiography of Scott Thorson, who lived with him for five years. Thorson was 18 when he met Liberace, who was then 57, but 42-year-old Matt Damon plays him with boyish conviction. He is, however – as Thorson was in life – perpetually hovering in Liberace's purple velvet shadow, dominated and outshone by the showman's glittering presence. Positioned permanently at centre stage, festooned with baubles, Douglas as Liberace is extraordinary.

At the press conference for Behind the Candelabra at Cannes, where the film was a hit, Douglas misted over as he recalled his gratitude when Soderbergh asked him to play the role. "Because, you know, I hadn't worked for two or three years. I wasn't sure if I had a career. And here was one of the best things I'd ever got. I had a career again, I could go back to work, I had something to focus on. I'd had cancer issues, my oldest son is incarcerated in federal prison and so there are a few things that have been going on, you know. So this was a nice break, just starting a project with really good people. This is the icing on the cake, that it's turned out as well as it has."

Douglas had been feeling unwell for nine months when a Canadian doctor found a lump at the base of his tongue the size of a walnut. It was cancer of the throat, advanced to stage four (as Douglas puts it, "there is no stage five"). Even so, he never admitted the likelihood that he would die. That was in 2010; he was still working the chat shows to promote Oliver Stone's Wall Street sequel Money Never Sleeps and Solitary Man after he started chemotherapy. The Liberace project was on the table. Then his weight plummeted. "It's rough, very rough. I just didn't think about it much," he says. "I said, 'I can't dwell on it, being out of my control', so it was just the killing of practically every other cell in my body with the amount of radiation and chemo they're feeding you. But it worked."

There is an eerie moment in Behind the Candelabra when Liberace is dying of an AIDS-related illness; Douglas, who has been plumped, smoothed and extravagantly bewigged throughout the film, is suddenly shown to be as withered and frail as he had so recently been in real life. Was that difficult? "I know it bothered my father a lot. I know it did," he says. Kirk Douglas, now 95, came close to death himself 12 years ago when he had a stroke. "I don't know exactly how, but when he saw the picture he didn't have a lot to say."

One of the advantages he had playing Liberace, Douglas says, was that circumstances conspired to give him so much time to think about it. "I had played gay once on Will and Grace in a guest spot on the show but, yeah, where do you start? How are we going to do this? You know, he was a big guy, a big Pole with a broad chest and I was worried about how to figure that out. Matt had a little bit of an advantage in that people didn't know Scott, but people knew Liberace and could make a comparison. I'm not an impersonator, but I worked on the voice first, then we started with piano lessons."

Douglas was declared clear of the cancer, subject to monitoring, in 2011. He was keen to start work immediately, but Soderbergh and Damon set another delay. "These guys were nice enough to say they had other things – well, they did have other projects to do, but I'm sure it was because they took a look at me and knew I wasn't ready. I thought I was because I was clean, but I was weak and thin. It's like starting over again."

At the time, he wondered whether his illness had been exacerbated by his anxiety and guilt about his eldest son's arrest. Cameron Douglas, now 34, is the child of his first marriage to Diandra Luker, a diplomat's daughter who was said to resent the all-consuming nature of the movie business.

By 1992, when Douglas went into rehab, his drinking and philandering had driven the marriage into the ground; at the same time, his son was expelled from school for dealing in marijuana. In 2009, he was arrested for dealing in crystal meth to support a heavy addiction to heroin and sentenced to five years' jail, which was almost doubled when he tested positive for opiates just as he was supposed to start a nine-month rehabilitation program.

Douglas acknowledges he put his career well ahead of fatherhood when Cameron was younger, just as his own father, who left his mother and went to Hollywood when he was six, had done. Cameron tried to follow his father and grandfather into acting, appearing with both of them in It Runs in the Family, directed by Fred Schepisi, about a dysfunctional New York family, but not much came of it. His father has been determined to do things differently with his second family. "I'm sure if he could breastfeed, he would have," Zeta-Jones told Vanity Fair.

She needed support, too. At the end of April, she entered treatment for bipolar disorder. Three weeks later, Douglas was at Cannes to present Behind the Candelabra. "She's great, thank you, she's doing fine," he says when asked about her. "It's a slippery slope, this bipolar stuff. I think you need to be careful. Sometimes you can think you don't need any meds at all, forget your meds and then all of a sudden you find yourself on a real ride. So she's fine, she's got herself stable. I can't wait to see her."

It probably wasn't worry that made that lump grow in his mouth, but it probably wasn't oral sex, either. "Without wanting to get too specific, this particular cancer is caused by HPV [human papillomavirus], which actually comes about from cunnilingus," he told the The Guardian newspaper.

In further dispatches, The Guardian made it clear that the sort of HPV virus associated with cancers of the mouth was usually transferred from the genitals, but just as clear that almost every sexually active adult would have come into contact with it. The body generally throws it off, the paper said, but the use of alcohol and tobacco – both of which Douglas has consumed in princely fashion – would get in the way of that process. The root cause of Douglas' cancer remains vague. Troubles, as they say, never come singly.

If anyone can maintain good cheer, however, it's Douglas. Liberace's forte as an entertainer, he says, was to invite people to enjoy the show as much as he did. He was the first person on television, Douglas says, to look straight into the camera, as if he were looking at the viewer, with that winning smile.

"He loved what he was doing so much and it came out to everybody else, both on stage and on television," he says. "When he played piano and everything else, you were captivated by how muchhe loved it. "How I found that was to think that I'm the luckiest guy in the world. I beat cancer, I've got the best part I ever had, God is good! That was the feeling. He loved beautiful things and when things got ugly or difficult, he shut down."

Once again, it seems the actor and his chosen character are about to become a single inextricable entity; nobody would ever imagine someone as comprehensively heterosexual as Michael Douglas being a closeted gay entertainer, but when he says he feels "blessed and fortunate that I'm alive", you see the glow of Liberace's effusiveness light his face. And that charm, of course, that makes us like him. That always works a treat.

Behind the Candelabra opens on July 25.