The former artist contacted Ono while she was making the 2009 film, which tells the story of the star's formative years in Liverpool, England, as she wanted to use the Beatles legend's song Mother in the picture.
Ono admits she felt wary about Taylor-Wood's movie, and was overjoyed when she saw the final cut.
In an interview by Taylor-Wood for British newspaper The Observer, Ono says of the director, "She had so much talent and incredible energy. She wanted me to give her the rights to use John's anthem Mother in her film.
"I thought, I'd like to see that film and was flabbergasted by it because it was so beautiful. But I must have a very strong prejudice about Englishwomen because I thought, how can a woman make this thing? It was a very bad way of reacting.
"And then I saw her and she is not a teenager but looked like a teenager and I thought, what is she doing? This is a miracle. I was impressed. Since then, I have got to know her way of life and it is incredible." (CL/WNSOBS/ZN)