The style icon struck up a close Bond with the designer - who committed suicide in last February - but confesses she was initially reluctant to meet him.
She said: "I admired him and didn't want to meet him because I am quite shy, but Isabella Blow said I must. But I didn't want to be a groupie. It had to happen organically. You don't have to know someone to love their work."
However, she admits Alexander - real name Lee - was little more enthusiastic when he first saw Daphne.
She told W magazine: "One day, he saw me walking across the street in his kimono and he ran up to me and said, 'I'm the person you don't want to meet!' We went to a pub and hit it off. Of course after that I was so irritated not to have known him before!"
Following Alexander's death, Daphne was one of several people from The Fashion world to pay tribute to him.