It's about a young girl who has a mean mother so she's always in her room listening to old records, when her mother tells her to stop playing the records she realizes it's her daughter singing. This girl sings like the different singers she was listening too. She performs in a lounge and when she changes her voice to a different singer, her persona changes as well. She impersonates people like Mae West and Eartha Kit, I think. I think the girl may have been from England ,not sure.

Could be Little Voice.

Oh yes! Little Voice, that was it! Thanks.