Trying to find the title of a movie I saw on TV in England between 1983 and 1987. It may be English or American.

It had something to do with a couple in an apartment and an old woman and a cage full of birds (parakeets? budgies? possibly canaries), who were found with all their necks broken.
There was something about a strange time line, they thought the apartment was haunted, but she turned out to be renting it after them.
Sort of a mild horror, but left me with some vivid imagery. Primarily that the whole film was sunny and bright and generally the opposite of a scary film.