****"let a woman in my life" does not necessarily mean movement. It can mean "inside" his life, like in his soup, in his fridge, in his bed, or in his head.****
Your phrasing confuses me, especially what you wrote about movement. Of course, Higgins means he will never allow a woman to have a place in his life -- i.e., to be inside it. Anyway, bottom line, "I shall never let a woman into my life" or "I shall never have a woman in life" both sound and read as correct to me, whereas "I shall never let a woman in my life" does not.