Now, at 52, she is still beautiful, but rather less feted. She lives in a small rented flat in an unlovely London suburb, just across from the grey concrete bulk of the Northolt Swimarama leisure centre, with her daughter Natalia and her sheltie dog Sukie. She still looks like a film star, with golden hair, lovely green eyes and fantastic legs, but these days she is busy not with acting - although she has recently had "talks" with some American television companies - but with fighting the latest stage in a court battle for child support from Natalia's father. It's a battle that has occupied her on and off for the past 15 years.
Her determination to get to Hollywood sounds itself like an improbable film plot. Born plain Suzanna Smith, she decided she was going to be a star at the age of five. She was dyslexic but, she says, "Years ago they didn't call it dyslexic - they just said you were thick. So I had to work out very early what I wanted to be in spite of it." She was encouraged by her father, a professional gambler, who died when she was six. (She never had a good relationship with her mother, a millionairess property developer.)
Her father had told his daughter that Vivien Leigh was her godmother, so at the age of 11 she trotted round the corner from her mother's house in Cadogan Square to Vivien Leigh's house in Eaton Place and introduced herself. "She said she had known my father, though she had been to hundreds of christenings and didn't remember mine. It was about 15 years after she'd done Gone with the Wind and she was stunning, beautiful and slender with dark hair. She said she didn't mind a bit if I used her name." So Suzanna Smith became Suzanna Leigh and secured a few acting lessons into the bargain. "It was really exciting. She was so fantastic to me. She said that so many of my dreams seemed like hers." (A black and white photo of Vivien Leigh still hangs in her kitchen.)
Suzanna's drama school career lasted all of two terms. "I didn't feel I could afford the whole three years for the course - in those days it was all based on youth, there was no chance in Hollywood to turn up at 22," she recalls. "You had to hit it quick when you were very young. If you were lucky it lasted a little bit of time, then you'd disappear. Nowadays it's much better."
She started her professional life with bit parts in The Saint, graduated to leading glamour roles, and was given her own television series in France. Then came her big chance: her agent rang to tell her that Hal Wallis, the famous Hollywood producer, was in England looking for the new Shirley MacLaine. Faking a stomach upset, she rushed off the Paris set, drove at speed to the airport, jumped on a plane to London, rushed to the Dorchester where he was staying and banged on his door to tell him "I'm the one you're looking for". "There'd be an army of secretaries to stop you doing that today," she says, with a yelp of laughter. "It just wouldn't happen."
Things happened quickly after that: Suzanna was whisked away to Hollywood, and the place lived up to its reputation. She still bubbles with joy at the memory of her first day on the set: she was 19 at the time. "I went through the gates at Paramount and for me it was fantastic. My first day in the studio this big Caddy came along with the chauffeur. It happened exactly the way it did in Sunset Boulevard. I thought `That's it, I need no more'. It's the most amazing feeling when all your dreams come true."
One of her most enduring memories of Hollywood is of working opposite Elvis Presley on Paradise Hawaiian Style in 1966. She and Presley were allowed to meet only on the set to avoid any hint of scandal, but one day, in front of photographers, Presley swept her up and kissed her. The photos went round the world. "That won't do your career any harm, baby," drawled the King. She was with Presley when Steve McQueen called her over to the adjacent set where he was filming and introduced himself. "For anybody of my age that was it: working with Elvis and having Steve McQueen chatting you up. I thought `I'd die happy right now'."
But the Hollywood dream did not last. Suzanna was scheduled to make another film with Presley. "Then out of the blue came an edict from the Screen Actors' Guild saying that I couldn't take the part. British Equity had refused to allow Charlton Heston to film his scenes as Gordon of Khartoum in Britain, so the Guild had retaliated by making it very difficult for British actors to get parts in Hollywood," she explains. "My mentor, Hal Wallis, said that union members were so opposed to me that they were throwing darts at my picture at the Guild's Beverly Hills offices."
Assuming it would take a while to sort out the problem, Suzanna flew back to Europe. "With hindsight I should have just stuck it out," she says. "I was supposed to do all these other pictures. It would have meant being out of work just sitting there. But when you're 20 and you're getting so many offers from Europe - I really couldn't believe that between Hal Wallis and Elvis they wouldn't be able to sort it out. My agent had died. So I went back to England."
She still lived the high life, however, mixing in London's showbusiness circles and working in movies, and living in exclusive Belgravia. She did some films in Europe, England and the West Indies. "And that was it really." She met Tim Hue-Williams, to be the father of her daughter, Natalia, at Ascot in 1972. This led to a 10-year relationship which ended when Hue-Williams deserted her for a rich heiress, his best friend's fiancee, when she was four months pregnant. Hue-Williams denied paternity and she had to submit her baby to a DNA test. Since then he has failed to contribute to his daughter's keep, ignoring court orders and pleading poverty.
Suzanna wanted to concentrate on motherhood and had let her acting career lapse. "I'd made a decision that I wanted a baby and it took years and years. I lost a couple during that time, and Natalia was three months premature when she was born." She had started an interior design firm which failed when a crooked lawyer cheated her - he later ended up in prison for fraud. It was now that her real financial problems began. Suzanna, now a single mother, initially supported them by selling her possessions and jewellery. ("Luckily I had quite a lot.") Natalia was very poorly when she was born and at the age of six she became seriously ill. Suzanna took her to Switzerland for several months to recuperate. By their return to England she'd lost all her assets. "I thought, `It's only money and I have my daughter'," she says. "Photographs are important. Everything else is replaceable."
Through the late Eighties and early Nineties she had an amazing stream of jobs. She hired a room in a library in Mayfair and gave lessons in etiquette. She ran speech and diction classes. And she sold the Encyclopedia Britannica at Heathrow Airport. "Being dyslexic I'd say to people things like `I won't bore you with the books' - if they took gold bindings I'd make quite a lot of money." By now she had lost her home in Belgravia, and had moved on, through a flat in Regent's Park that was sold over her head, passing through an ex-council flat, relying on benefit at various times.
But she isn't planning to stay in Northolt. When Natalia has done her GCSEs later this year she intends to move back to the US to restart her career. She has already been negotiating her own local morning television show in Memphis, where she hopes to settle. And she has written her memoirs, Paradise Suzanna Style.
Will the gulf between Northolt and new fame and fortune in the US be bridgeable? Let's hope so. Although she seems indestructibly optimistic the past few years must have been hard. But Suzanna Leigh says she has just one regret. "I should have stayed in Hollywood. But you don't know what's going to happen. Who knows, if I'd stayed in Hollywood I might have died! Sharon Tate was my best friend; perhaps I'd have been at that lunch where the guests were murdered by Charles Manson. I could have been dead in 1969. My god, aren't I lucky! I made it this far!"
IN HER OWN WORDS...
On being an English actress in the US
Just being English gives you a real edge; they love the English. They have this idea that you're walking talent anyway. I'm sure Kate Winslet is finding the magic. It's so hard to get anything together over here; you just have to go where the real work is.
On Steve McQueen teaching her to shoot
He told me the biggest worry was getting to the point where you shoot too fast, before the gun's even out of the holster, and pepper your leg. He told me a great list of people who'd done this. I was quite good, but I said, "I promise you that is not going to be one of my problems."
On Elvis Presley's peacocks
Elvis had never met anyone quite like me and he loved to hear me tell stories. He was very hot on security, and I told him about keeping a pair of peacocks to make a noise if any intruders approach. Years later I went to Gracelands and found he had got his own peacocks. Of course, being Elvis, he didn't have a pair of peacocks, he had a flock of them. Apparently the noise was mindblowing.
On being a Catholic
I went through a very religious phase. I used to go to the cathedral a lot and say: "This is not on! This is not on, you know! When I prayed for a very small baby and said `I don't care how small my baby is', I didn't mean weighing less than one pound!"
My father was a successful gambler and I've always had a bit of the gambler in me. Luck is part of it but you make your own luck.