Not in her ‘ex’ files

“THE X-Files” star Gillian Anderson is quietly dating Peter Morgan — the Oscar-nominated UK writer behind “The Queen” and “Frost/Nixon” — sources exclusively tell Page Six. London-based Anderson was in town this week to launch a book with Jennifer Nadel, “We: A Manifesto for Women Everywhere,” and was with Morgan at a MoMA premiere of his new Netflix series, “The Crown,” on Sunday. “She was telling friends she’s dating the writer from ‘The Crown,’ ” said a source. Morgan reportedly separated from his wife of 19 years, Lila Schwarzenberg, aka Princess Anna Carolina zu Schwarzenberg. She’s an Austrian journalist with a column Morgan has called, “about our manky marriage.” She reportedly wrote: “Peter . . . always says you can gauge the state of our marriage on the number of fish fingers he gets served . . . I served him the leftovers of the kids’ meal . . . He took one look and said: ‘I am neither 5 years old nor a f - - king penguin.’ ” The couple has five kids, and Morgan once joked: “People come to our house . . . and they leave so happy not to be us.” Anderson’s been married twice and has three kids. She split with partner of six years Mark Griffiths in 2012. Reps didn’t comment, and the truth isn’t yet out there as to whether Anderson serves fish fingers.