Liza is late. Of course. The world moves through the foyer of a chichi central London hotel and every so often the lift opens and disgorges passengers, most of whom are lugging large lights, camera equipment or makeup bags. They begin to pile their stuff up in the lobby and then return to the lift to ascend once more. As the lift is roughly the size of a coffin, they make a lot of trips.

Judging from the amount of equipment now amassing at my feet, they have been remaking Ben-Hur up there. In its midst, there is a box. It is full of papers and has a label on the outside. The label reads "Liza Minnelli".

Just as my anticipation is about to curdle through boredom into irritation, Ms Minnelli is ready: she will see me now. Only, says the publicist, could I avoid questions along the lines of how does she remain so positive about her life, etc? Apparently Ms Minnelli can't see why she shouldn't be positive. As the publicist is wearing the weary look of a man who expects to be shot at dawn, I agree to this slightly odd request. Anyway, being 60, and one of the last of the old-time stars, an heiress to Hollywood royalty, Liza has done a few interviews in her time and by now there must be questions that simply irritate, odd or not. And I can see how questions about positivity might lead to questions about the negative in her life . . .

Minnelli is the only child of two Oscar winners, Judy Garland and Vincente Minnelli, to win an Oscar herself. She is also one of the few artists to have won all four of the American entertainment industry's top awards - the Grammy, the Emmy, the Tony and the Oscar. But her personal life hasn't just been a car crash, it has been a pile-up. There are the manifold addiction issues, the four failed marriages and many doomed love affairs, the tricky relationship with her mother, and the brush with death (she developed life-threatening encephalitis six years ago).

But here we are at Ms Minnelli's suite and here we are at Ms Minnelli herself. Dressed entirely in black - a fleecy top and what I like to imagine are palazzo pants - she is propped up on an overstuffed couch, the likes of which you only find in hotels. Her eyes are wide and bright. Her makeup is thick and flawless. There is a beauty spot planted on her cheekbone. She looks exactly like herself and if she hasn't had any work, she looks great for 60. She also looks not unlike a panda.

Minnelli holds in her hand a cigarette. In the saucer she is using as an ashtray, there are two crumpled stubs. She claimed recently that smoking was her only remaining vice. Does she miss the others? She looks inscrutable. I wonder if this is because she can't move her face. "Darling," she says, "all of us spend so much time on stuff that is not worthwhile. I think, as you get older, you learn more about what's worthwhile and what isn't. You've got the experience."

This doesn't really answer the question, but that, it transpires, is something I will have to get used to. (It also turns out that she can move her face). Along with the panda, there is an elephant in the room. An elephant called David Gest. Liza's fourth husband is off limits as a subject. Minnelli is, according to her publicist, legally forbidden to talk about him. At their 2002 wedding, at which Michael Jackson was best man and Elizabeth Taylor matron of honour, Gest made this declaration to Minnelli: "You make me a complete person. You are everything to me and I will love you for ever." He then planted a now legendary kiss on Minnelli (the expression "face sucking" springs to mind).

Sixteen months later, the marriage was over and the pair are currently slinging quite an extraordinary amount of mud at each other. In 2003, Gest accused his wife of assaulting him repeatedly. Meanwhile Minnelli's lawyers have maintained she was in fear of her life during their time together. Gest says her attacks have left him in constant pain, requiring a cocktail of medication, and suffering from anorexia. Moreover, he claims she bit one of her employees while drunk.

Minnelli, for her part, has claimed that Gest has invented his ailments, that her "attacks" were self-defence and that he was trying to poison and control her with drugs. Then there is another lawsuit involving the chauffeur ... and stories about Minnelli's dog being put down while she was out shopping. And that is before you even get to the whole question mark over Gest's sexuality, which few people seem to regard as resolutely heterosexual. Hardly the most dignified of divorces. Indeed, even the judge in the case has said that she has had enough of their "whiny garbage". "It's undignified and it will stop," she said. Even if she were allowed to talk about the whole sorry mess, you can't imagine Minnelli offering to and, frankly, it would seem a little prurient to ask: "So, Liza, did you batter your gay husband?"

Instead, with Gest a non-subject, I am left reading everything into anything she says, wondering if, by saying such-and-such, she means something else. As is often the case with someone who has undergone rehab or therapy, much of what Minnelli says sounds profound as you are listening to her, but it doesn't stand up to close scrutiny later.

Minnelli is in London to promote the DVD release of her 1972 concert, Liza with a Z. Directed by Bob Fosse, filmed on one night on Broadway, and broadcast on American television, it shows Minnelli at her very peak. She is luminous, energetic, goofy-sexy and what the French describe as jolie-laide. Never conventionally beautiful, she is nevertheless mesmerising to watch. She inhabits the stage effortlessly and belts out her signature songs, including a medley from Cabaret and, of course, Liza with a Z, written by Fred Ebb just for her.

It is more than 30 years ago, but seems, she says, like yesterday. She says that at a gala screening the previous night, she sat in the cinema, "Breathing with it. I was sitting there and my hands were sweating. I don't want to forget it. I won too many awards to forget it." However, she rarely watches herself. "I'm always looking at the next thing. I'm too curious to look back ... it's very hard to be unhappy when you're curious and grateful. You're busy. You don't have time to be unhappy. My biggest talent is I know who is more talented than I am. I find them and I go to them, and I learn."

Minnelli is relentlessly upbeat. The show must go on, it seems. "My family's been in showbusiness since the 1700s," she says. "I traced them. I'm bred to this. Like a racehorse. A thoroughbred. Look at my parents, my God. But it was my curiosity that made me do this. Because you could also say, look at Frank Sinatra Jr." She wrinkles her nose. "It's not like a natural thing that happens. You gotta work." (Her point presumably being that Sinatra Jr has never managed to escape his father's shadow.)

Work is something Minnelli has certainly done. Even now, she does two hours of jazz dance every morning, "same as I ever did". Dancing is a great love, though she wanted to be an ice skater for a long time. "I trained to be a championship skater. I don't do that any more but I watch it all the time. I never miss the championships. I don't want to do that any more with false hips and a wired-up knee. It's hard to find rinks now, though I love to watch at the Rockefeller Center. And it's gorgeous in [Central] park."

She says she has no intention of retiring. What advice would 2006 Liza give to 1972 Liza? "That's a waste of time to do that," she says. "It's a waste of time to think about what I should have done and what I didn't. I really believe in that. That's how I react to the if-onlys of life. To moan and groan about something I shouldn't have done, could have done, might have done ... who knows? It is what it is. You got what you got. I live my life one day at a time."

That is what you have to do, when you are a recovering addict: live one day at a time. But it is fair to say that a bit of forward planning might not have gone astray in Minnelli's life. She first appeared on film, aged 14 months, in In The Good Old Summertime alongside her mother. She appeared, opposite Garland, on stage at the London Palladium in 1964, aged 18, and this is widely seen as the tipping point in her career. Then came her Oscar-winning turn as Sally Bowles in Cabaret in 1972. But with every high, lows accumulated. There were her ex-husbands, pre-Gest - Peter Allen, Jack Haley Jr and Mark Gero. There were her battles with drink, drugs and her weight. And in 2000, there was the encephalitis. It was while recovering from the condition, and weighing 17 stone, that she met Gest. It was a rollercoaster, by any standard.

Ever the optimist - we avoid the word positive - Minnelli counters with a suitably life- affirming story. "My dance teacher, who's a brilliant man called Luigi, had a terrible car accident and was in a coma for four months. He really went through it - his eyes fell out and they put them back in. He woke up and he couldn't move. I had brain encephalitis and I woke up and I couldn't move. When I got moving, after they told me I wouldn't, I went to him and I said, 'Papa' - I call him Papa - 'Will I dance again?' And he said, 'Sure.' I think it's all possible. And if you think about it, and you really want to do it, you can do it. And if it's worth really doing."

While it has been reported that she has been a little incoherent in previous interviews, she is far from it today. As we talk of her love of New York, and how Los Angeles is a bunch of suburbs in search of a city, she proclaims her love of Dorothy Parker. "She was wonderful. What's that great one? Razors pain you, rivers are damp, acids stain you and drugs cause cramp ..." She is fond of Las Vegas too, where she is due to perform after making an appearance in the American TV show Law and Order: Criminal Intent (following her rather fine cameo in the comedy Arrested Development).

"I can't wait to see Vegas again. I remember the first time I went - I was nine and my mom was playing there. I was at the pool all day, along with everyone else, and then, at five o'clock, everyone went inside to dress. I haven't been in about five years. You have to high-jump the baby carriages in the casino now. Before, you used to walk through and everyone was in tuxedos but now, no one gets dressed up. People come to see shows in shorts and things. It's been made into a family town, which is good economically, but what's missing is the mystery, that danger."

We talk about how America has changed since 9/11. "It affected all of us," she says. "We understood what real fear is. The thing that everyone in this country has always known - what with IRA bombs and everything - we never had that. Well, we do now. It was really scary, but it really showed the spirit of New York. The song that I sing - New York, New York - became an anthem then. I went down there and sang then."

Then the air in the room changes suddenly. "I gotta get going, darling," she says. "I really do." Minnelli rises to her feet and shakes my hand. The interview, which has also felt like something of a rollercoaster, is over. I am disoriented and she is in the next room waiting for me to leave. I consider making her wait a long time but escape to the corridor and then to the coffin-sized lift. It feels big without a panda or an elephant in it

· Liza with a Z is out on DVD now.