Cats do an amazing amount of damage to the bird population. And it's not as if they need the food; it's just the instinct to catch things. Do you know who owns this cat? Is there a way to ask them to keep the cat indoors (for the sake of the cat as much as the wildlife)? I know - I hear it every day - "I can't keep my cat inside. Fluffy will get upset." That's a bunch of bird doo. Fluffy will be safer from cars and disease and can be happily entertained inside by playing with her human family.
Sorry, I get so upset about this. Then again, I'm one of the people that has to deal with the death and injuries of cat caught birds, squirrels and bunnies.
If talking to the cat owner is not a possibility, then try hanging the flower pots elsewhere, away from railings and bushes so the cats can't reach them. Finches love to nest in hanging plants and will gladly nestle down deep under the leaves and flowers. It's a great chance to see baby birds grow up and fledge. But do hang the pots under the eaves well away from perching spots for the cats.