By 1990, the edgy co-star had netted his first major leading role as the most violent, volatile anti-hero of them all - Vincent Mancini in The Godfather Part III. Hailed both on screen and off as a pretender to Al Pacino's throne, Garcia gave a passionate performance, chewed off Joe Mantegna's ear and picked up an Oscar for Best Supporting Actor. But while Vincent won power over the Corleone clan, Garcia himself never quite ascended into Hollywood's screen royalty. "The first wave of attention one gets as a movie star is overwhelming," says the actor. "For that month, or that 15 minutes, you become everyone's focus. But I resisted it. I think it's my nature. When the spotlight's on me, I tend to step out of it."
Nearly a decade on from Coppola's ill-fated sequel, Garcia seems comfortable away from the Hollywood glare. A practising Catholic and fiercely traditional family man, he's happy to devote himself to Marivi, his wife of 17 years ("We met in a bar. I proposed that night. I was struck by the thunderbolt, you might say"), and their three girls Dominik, 14, Daniella, 10, and Alessandra, six. They're waiting at the hotel for their dad to finish his interview so that they can see London. "All we do on these trips is talk and eat," says Garcia, with a flash of white teeth. "Tonight we're going to eat."
Beneath his expensive, immaculately-cut suit, the lean anti-hero has filled out. His face seems rounder than before, soft around the edges. Is it possible that Garcia has lost his hunger for acting? "Absolutely not," says the star, although years in the business have taught him a trick or two. "When you're younger and they say `action', you run through the wall. As you get older you can sort of metamorphose yourself through the wall. Or you can open the door and just walk to the other side. That doesn't mean I've lost my passion. It's just different. "I still have a great appetite for acting. I'm still hungry."
Born Andres Arturo Garcia Menendez, Garcia left his home town of Havana when he was five. Fleeing Castro's regime, his parents settled in Miami Beach with "little more than their human rights". After a brief period of isolation when he couldn't speak the language, the young Garcia "learnt how to fight in English" and began school, where he was coached in basketball by Mickey Rourke ("Mickey had a rough upbringing, and that always shapes you, but to me he's always been a very dear friend"). Never growing tall enough to achieve his hoop dreams, Garcia decided instead to study theatre at Florida University.
After performing, penniless, in Florida theatres, Garcia made the pilgrimage to Los Angeles in 1978. Loading trucks and working as a waiter (for one job he dressed up as a pirate, for the after-dinner entertainment at a Puerto Rican hotel) he did the rounds of low-rent agents, trying to get some representation. "They sort of analyse you, you know? `Cut your hair. Change the colour of your eyes. Change your name. How tall are you? Get lifts. Lose your Spanish accent.' Whatever. They dissect you, as if you were a product." At one audition, a female casting director asked Garcia to take his shirt off. "I will if you will," he quipped before sailing out through the door.
Despite his sensuous good looks, with eyes one excited journalist described as "burnt sienna", Garcia has continued to resist roles as the Latin lover, and to avoid gratuitous nudity. "I prefer to be a romantic," says the man who was later to keep his T-shirt on throughout a love scene with Bridget Fonda during the filming of The Godfather Part III.
These days, of course, Garcia is enough of a player to pick and choose his own projects. In his latest movie, Just The Ticket, he escapes a career spent playing cops and robbers to cast himself as a flaky, New York ticket tout. Getting into character, Garcia hit the back streets of Times Square, "scalping" tickets for Cats while a hidden camera recorded the scenes for the film. "This woman came up to me," he smiles. "She said, `Andy, you're a very fine actor. You shouldn't have to be doing this'."
With a star on the Hollywood walk of fame and a fleet of workers just putting the finishing touches to the landscaped garden of his mansion in Miami, Garcia can afford to laugh, and yet there is a sense in which the 43-year-old's career is, if not exactly on the skids, then suffering a certain comfortable dereliction. While not exactly down and out in Beverly Hills, Garcia seems to be retreating from the razor-sharp promise of his early roles. In the Nineties he played opposite a series of big name co-stars in a string of post-Godfather duds such as the serial killer thriller Jennifer 8 with Uma Thurman, and An Accidental Hero with Dustin Hoffman. Sure, he can still open a romantic drama, such as When a Man Loves a Woman opposite Meg Ryan, or work with a venerated director such as Sidney Lumet in Night Falls on Manhattan, but none of these films are anything more than solidly made, unmemorable Hollywood fare.
Garcia the actor/ producer shows even less savvy of what's likely to be box-office, but its hard to hate him for his vanity projects. No self- aggrandising Streisand, he makes hopelessly well-meaning movies about his Cuban ancestry, such as the soft-centred social comedy Steal Big, Steal Little, the elegiac drama The Disappearance of Garcia Lorca and The Lost City, his collaboration with the novelist and fellow Cuban exile, Guillermo Cabrera Infante. His directorial debut, Cachao... Como Su Ritmo No Hay Dos (Like his Rhythm, There is No Other) saw the star mamboing to the tunes of his childhood hero, the renowned Cuban bassist Israel Lopez, "Cachao".
"I can be attracted by anything in a script," says Garcia, "It doesn't take much for me to say `yes', but I need to fall in love with something. I did Steal Big, Steal Little because I always wanted to play a guy who grew avocados. My father used to grow avocados, so that was enough!" Garcia laughs. "You have an avocado tree in the script, I'll do it."
Apart from avocados, the thing that determines Garcia's career moves, of course, is the "moral priority" he gives his family. He avoids roles that would take him away from them on location shoots for too long, calls Marivi's job as a wife and mother "the hardest profession in the world" and skips Hollywood parties to "help the girls with their homework". In the La La land of sex-addicted leading men and Heidi Fleiss sleaze, Garcia is a rare breed indeed. Although he admits to a quick temper, his only vices appear to be the occasional cigar and an amateur passion for the bongos.
In 1990 Andy Garcia was voted star of the year by the National Association of Theatre Owners after his performances in Internal Affairs and The Godfather Part III. In 1998 he was voted Father of the Year by the Father's Day Council. There's no question which award is the bigger accolade, but ask him if he's put his career on the backburner for his family and he looks a little hurt.
"How much bigger star do I need to be? How much more famous? You know I just want to be able to do good work in the kind of things I want to be associated with, and provide a living for my family. It really doesn't get much more complicated than that."