The Calendar Girls actress, now 58, longed for a baby in her mid-40s but hated the thought of having a husband.
She told the Evening Standard that she eventually came to an agreement with her friend Benjamin Whitrow.
She said: "Ben and I walked on the beach one day as I laid out my terms. These included that I would not ask for anything, I wouldn't want to live with him, or marry him, would never ask for money for the child.
"If Ben could take all that on board, I said, then his offer to fulfil my wish for a child would be wonderful."
Imrie added that Whitrow, an actor, has since been "a marvellous father" to her son Angus, now 16.
Imrie is due to appear soon in the ITV version of Titanic, written by Julian Fellowes, who has previously revealed that he is "terrified" at the prospect of stepping into James Cameron's shoes.