Miss Tyson is far too famous to talk. Eyes hidden by massive wraparound shades, she just strides past on her way to the pool where Brad and Angelina are waiting. In another life.
That is the life Cathy Tyson could have been living, had she had done things differently after the film Mona Lisa made her a star at 20. "Oh, I have a lot of regrets about all that," she surprises me by saying in this life, the real one in which she seems prepared to talk for as long as anyone could wish, in a cold and empty cake shop in north London.
LA is far away. Two decades have passed. Tyson still has extraordinary presence, though. Her lime-green dress, leaving her arms bare, defies the rainy day. She speaks in a deep, clipped voice that says "I Am a Serious Actress". And she is one of our best, who has played many of the great stage roles since 1986, when Neil Jordan's film gave her Hollywood potential.
"I act as if I don't have any regrets at all about my life, but of course I have," says the woman who acted Bob Hoskins off the screen. The critics raved about the newcomer's remarkable skill and androgynous beauty. The daughter of a man from Trinidad and an Irish woman from Liverpool, she had a look that was becoming hugely marketable: Tyson could have been as big as Halle Berry, drinking tequilas under the LA sun instead of which she is sipping lukewarm cappuccino near her home, remembering turning down big roles.
"I didn't speak about my fears at the time," she says, and this is the first time she has done so since. "I was frightened Hollywood was going to ask me to lose a lot of weight and change me. I am fiercely stubborn, really. I didn't want to be exploited and take my clothes off to sell the physical."
There were other reasons why she didn't take all her chances. Good, honourable ones she will talk about in a while, but they came at a cost. "For years I have had regret about what I haven't done there. It was killing me. The regret was a weight on my shoulders." That sounds like depression, but I'm only guessing. "Over the last few years I have been learning to let go of it. New challenges help."
The latest, and most unusual, is to play a tyrannical version of Herod in the BBC's live outside broadcast Liverpool Nativity next Sunday. It is a follow-up to 2006's Manchester Passion, which drew huge crowds and controversy for its odd use of modern pop songs from the city. This time the Beatles and the La's will provide tunes.
The angelic host will include Jennifer Ellison, an actress who could probably do with some advice from Tyson about how to become known for more than your looks.
Age has replaced Tyson's youthful street swagger with a calm magnificence. Her Herodia is a murderous minister in a police state who sends her forces to pursue the asylum-seeking Holy Family. She seems to begin our interview in character, retaining poise even when revealing that she has to sing "You Spin Me Round" by Dead or Alive, a high-camp helping of Eighties froth allegedly transformed by its use in this setting. "It's all about getting an asylum-seeker's private number, baby," she says, in an almost convincing way. "And the 'baby' is to do with Christ."
Of course it is. But isn't the BBC acting a bit like a trendy vicar by making Mary and Joseph into asylum-seekers? "I haven't seen many dramas about asylum-seekers," Tyson booms. "When do they get a bloody voice in our country? Why can't they be centre stage? God bless 'em." Joseph and Mary were asylum-seekers, she insists. "They had to flee Egypt. They fled a brutal regime."
Tyson is no innocent; she knows why the BBC would be attracted to casting her in this role. "It's a black person tyrannising another black person's life, not a white person. Perfect for the BBC." So she must also know that, despite what she says, it's not some foreign dictator but Labour's approach to asylum-seekers that comes to mind when she says Herodia "goes for the weakest members of society to drum up support".
She expects to feel strange when her character addresses the crowds from St George's Hall, in the city where she grew up. "My family are outsiders," she says. "So it's ironic that I'm now saying lines like, 'Go back to where you came from!' That is what was levelled at me as a child."
Tyson's father, a lawyer in Trinidad, was mostly absent when she was growing up. Her mother was a social worker in Toxteth. "It was a vibrant place, but the black people were anti-white and the white people were anti-black." That put her right in the middle then? "Hmm." Asked what Liverpool gave her, she remembers the seaside, "the beauty of the Wirral", the mountains of north Wales and discos run by the Catholic church and the police. "No alcohol, just music and lots of beautiful boys I could never access." Why not? "I didn't look like a Sindy doll."
Mountains, music and the sea are all means of escape. That's what she did at the age of 13. "Liverpool was just rows and rows of bleak estates and I thought, 'I've got to get out of here.'" She fled to London with a friend. "We found a hotel and got jobs. I changed my name, began a new life. Some girls are very independent, aren't they?"
Three things happen while Tyson says this. Her accent becomes dramatically more Scouse. She starts worrying at the back of her neck, elbow up in the air. There's something vulnerable about the sight of an armpit. And her eyes glisten. She excuses herself for five minutes, then explains this is not something she has talked about much. "I went to work as a chambermaid. I was not very good at it! I managed to clean one room in a day." There were appeals for the two missing girls, and police searched London hotels. One officer spotted her in a corridor. "He said, 'Are you Cathy Tyson?' I said, 'Yeah.' Then I went, 'No, I'm not, I'm Stacey Smith!' But he had caught me off guard."
She is grateful now. "I was in a lot of danger. People tried to abuse me twice. My Catholic upbringing saved me on that account: I was like, 'No, aren't we supposed to be married?'"
When she returned after a week "such a long time at 13" her mother barely mentioned it and her friend never spoke to her again. "Maybe she was told not to. It's bringing up emotions in me now. Gratitude for the policeman ... I've never felt that before."
If he saved her, acting changed her life first at school, then at the Everyman Theatre in Liverpool. "It got me out of trouble. I was a very cheeky schoolgirl but I started to find my voice in drama." She pauses, knowing she has a good line. "Liverpool gave me a mouth. But Shakespeare gave me a voice."
The Bard also kept her away from Hollywood, after Mona Lisa. "I wanted to go back and do the great plays of the country." She has, too, for the Royal Shakespeare Company and others. "I've done Pygmalion, Educating Rita, The Merchant of Venice..." Her performances have been critically acclaimed. She has also made a lot of very good television, including Band of Gold. Far from being a disaster, her career saw her named alongside Lennon and McCartney as one of the 800 people who put Liverpool on the map during its first 800 years.
The other good reason she didn't move to America was Jack, the son she had 19 years ago with her fellow actor and then husband Craig Charles. They got divorced, and Charles went on to star in Red Dwarf and a series of tabloid scandals involving sex, drugs and chat lines. But Jack has been the love of Tyson's life and she has no regrets about turning down any work to be with him. "I owe a lot to my son. His love and his personality, and being a mother, shaped my work."
Something strange happens now, as we wind up. Unprompted, Tyson goes into a thank-you speech. "I'd like to dedicate this interview to my friends and my family," she says. "They have been there through the most difficult times. I wouldn't be here without them." Halle Berry would expect an Oscar after that. Cathy Tyson, letting her shoulders drop and smiling for the first time, seems happy with her cappuccino.
Further viewing: 'Liverpool Nativity' is shown at 8pm on 16 December, BBC3, and 10.45pm on 23 December, BBC1Reuse content