This was a movie in the 80’s or 90’s. A young girl is emotionally disturbed and a woman (a psychologist or social worker) is trying to help her. The girl keeps singing the clapping song- “my mummy told me, if I was goody, that she would buy me a rubber dolly”. Eventually the psychologist becomes affected by the girl’s madness, and at the end of the movie she sings the song too.
I’m not sure if this was a TV movie, and I think it may have been British but I’m not sure.
Any help is appreciated!