Annis and Fiennes, who have been together for over a decade, have often been heralded as one of the closest couples in Hollywood.
But brunette Cornelia Crisan, 31, claims the screen star has been using her to alleviate his loneliness and sexual frustration.
She tells Britain's Daily Mirror newspaper, "He wanted me to be there for him whenever he needed to talk, wanted a cuddle or to make love.
"Twice he told me he loved me... He was already with someone. He was a cheat."
Fiennes allegedly left a message for Crisan two weeks ago, saying, "I want some physical contact. I might be able to see you. I may come to London in the next couple of weeks."
The 43-year-old Harry Potter star started dating Annis, 61, in 1994, despite at the time being married to ER actress Alex Kingston.
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