“I went to visit him and ended up selling my return ticket and staying,” she said. “If I hadn’t gone, I wouldn’t have gotten The X-Files…but at that point I might have stopped and thought: ‘Actually do I want to live here? Am I not enjoying living in New York?’
“Right now my daughter’s planning a gap year and I’m hoping she will properly explore the world, but I keep thinking what happens if she meets somebody and that somebody lives somewhere else and she decides that actually what she wants to do is be with that person and go and start having kids.
“I’m encouraging her to follow her heart in big things rather than following men. The amount of time wasted on that… ridiculous.”
The X-files, which ran for nine seasons between 1993 and 2002, made her one of the biggest television stars in the world.
When the show ended, Anderson moved to London because that was where her then boyfriend was based.
“I wish I’d been more aware when I was her age of how lucky I was, how many choices I had,” she said.
“I would have looked at all the different potential paths open to me and expanded my world more.”
Her stardom as the agent also led to her to be named the “sexiest woman in the world” by FHM magazine in 1996 but in the interview she admits to “obsessing” with how she looked when she was younger.
She also reflected on how her looks had changed with age but ruled out plastic surgery, saying she would rather get old naturally, like Judi Dench and Charlotte Rampling, the actresses who she admires.
“Plastic surgery does cross my mind,” she said.
“I remember a couple of years ago looking in the mirror when I was putting on make-up for a play, I noticed some changes. I was so shocked that for a few seconds I convinced myself I’d eaten something I was allergic to. Then I realised: ‘No, that’s what happens.’
“There’s a lot about getting older that I’m still very much looking forward to. But there was a moment – more than a moment, a couple of days – of proper, full-fledged grieving over my youth and loss. Years lost and time wasted.”
It was during her time on the X-Files that she met her first husband, Clyde Klotz, an art director.
They divorced soon after Piper was born, however, when Anderson was 26.
She was later married for 18 months to the journalist Julian Ozanne before having two children, Oscar, now six and Felix, now four, with businessman Mark Griffiths. They separated last year and she is currently single.
Anderson – who returned to The X-Files 10 days after giving birth to Piper – said she was now determined to atone for what she saw as her mistakes with her daughter by fitting work round family.
“Being a mother second time round, I’m so more aware that my impact on my children’s entire lives starts when they are born and that what takes place between two through 10 is as important psychologically, emotionally, intellectually as what happens when they start going to whatever important school they’re going to and start experiencing that sort of learning,” she said.
Anderson is about to appear as DSI Stella Gibson in new BBC Two crime drama, The Fall, which starts on May 13.