Kubrick was fascinated by this story and tried to develop it into a film, but died before it was made. Steven Spielberg took up the project and AI: Artificial Intelligence came out in 2001. As a note, if you don’t want a spoiler DON’T read the Publisher’s Blurb at the top of the page, scroll down until you get the first line “In Mrs. Swinton’s garden…”.
First published in Harper’s Bazaar in 1969 and later anthologized.
Author website: http://brianaldiss.co.uk/