Straight On Till Morning (1972)

Shy Brenda Thompson writes naive children's stories to amuse herself. Stifled and desperate for a man of her own, she leaves Liverpool, telling her mom she's pregnant, and gets a job in a boutique in London. She moves in with the promiscuous but good-hearted Caroline but the mod set shuns her for her plain looks. Then she kidnaps a strange young man's dog, so as to perhaps get to know him while returning it. The young man turns out to be Peter, a psychopath with a predilection for killing beautiful things. He renames Brenda Wendy, and they start a hopeful, if strange, relationship. It might have a chance, if it weren't for Peter's murderous secrets.

IMDb: https://www.imdb.com/title/tt0069318