The Onegin director, who is the sister of actors Ralph and Joseph Fiennes, has three children with Tiffin - including son, Hero, who starred in Harry Potter and the Half-Blood Prince, and daughter, Mercy, who starred alongside Keira Knightley in The Duchess.
Last year (10), Fiennes admitted she "would love to get married", but Tiffin was strongly against the idea.
Now the pair has split - and Fiennes is already dating again.
She tells Britain's Daily Mail, "Very simply, we have mutually parted ways. Yes, I am with someone else - a Swiss-Arab businessman."