As a teenager, she preferred to immerse herself in TV reruns rather than bother with modern cinema. "I was into Love Story and Wizard Of Oz and all the other films they showed every Christmas. But that's my thing. I like films that make me cry or smile from my heart."
At the age of 18, Cheung was offered a modelling contract. Her agency then put her up for Miss World, where she got noticed, had a laugh in London and found "the Spanish-speaking girls especially friendly. It was so different to 'Miss Hong Kong', which, because it was a smaller competition, everyone thought they had a chance of winning. So everyone was bitchy and aggressive. Miss World was just funny."
The beauty pageant led to a movie contract - with the Shaw Brothers Studio of Hong Kong, where she made her debut, alongside Jackie Chan, in the massively successful Police Story. She became one of the hottest stars in the colony and found herself at the mercy of the press.
"The Hong Kong tabloids are worse than the English tabloids, if you believe it. They got their hands on some personal letters I wrote to a friend and printed them. Their defence was, 'We're concerned about you. We care about you. It's in the public interest.' It hurt me that they would do that, but it didn't damage me or my career in the end. I was just embarrassed for a whole week, seeing my face on the cover of all the papers."
Those tabloids now protray her as snobbish and ungrateful because she wants to be seen as an actress as opposed to a star.
"If I wanted to be a star, it would be easy. I would stick to the violent films and choose the huge ones with the big-name actor."
She seethes that the Hong Kong press expects its stars to pay for journalists to write positive articles about them. "The idea of being a 'star' is so tacky. Only De Niro carries it off. He's a star and an actor and you don't see him in the tabloids, or hear about his personal life. That's my dream - to be recognised for my acting and still be successful."
Irma Vep should be the one to do it. It's glossy and funky, yet the complexities are astounding. In one of its most puzzling, erotic scenes, a drunken, lonely Maggie dresses up in her rubber Irma Vep costume and creeps into the bathroom of a fellow hotel guest. She watches from the bathroom as a naked woman has a screaming row with her boyfriend on the phone. Maggie steals of a glass necklace then crawls out on to the roof and drops it ten floors down on to the filthy Paris street.