The actress and the director have been together for 11 years, and they are parents to two children, Billy, nine, and Nell, four, but they have never made their relationship official.
However, the Harry Potter star admits they have to consider exchanging vows for the sake of their kids because their son Billy only recently discovered his parents are not married.
Carter reveals the youngster assumed his parents had tied the knot after seeing a picture of his mother wearing a long dress on the set of the couple's 2007 movie Sweeney Todd: The Demon Barber of Fleet Street.
She tells British newspaper the Daily Mirror, ""Yes (they do want us to get married). Nell wants a dress, but actually, Billy was the one who was worried. He said, 'Are you part of our family?' And I said, 'Yes'. Then he said to me, 'But you were married. What about the wedding photo?' And, of course, he was referring to a photo of me in costume for Sweeney Todd, where Tim and I were just playing around. Billy thought that was our real wedding photo.""
Asked whether the couple will now be getting married for real, she adds, ""We might do.""