Bunny Lake Is Missing (1965)
Ann Lake has recently settled in England with her daughter, Bunny. When she goes to retrieve her daughter after the girl's first day at school, no one has any record of Bunny having been registered. When even the police can find no trace that the girl ever existed, they wonder if the child was only a fantasy of Ann's. When Ann's brother backs up the police's suspicions, she appears to be a mentally-disturbed individual. (IMDB Alfred Jingle)
"Ah the telephone that miracle of modern communication.
I often wonder why it is that we communicate so much
less with all these marvels at our disposal than we did
in a more primitive day without the wireless and the television."