actually i did hang some nest boxes for the budgies and noticed that they are not that much interested in the finches anymore .Nipper06 wrote: I let my parakeets (1 Budgie and 2 Bourkes) fly in my sunroom, where my finch cages are and there's never been a problem - and my Gouldians breed no problem. But my finches are in large flight cages and my keets are only "visitors" in that room. However, I recognize that Budgies can be aggressive, especially if they are crowded or in "breeding mode".
Perhaps if you hang some perches higher than your finch cages, the budgies will lose interest? Another thought: the budgies might be "interested" in the cages because they are like nest boxes. Maybe hang up some proper budgie nest boxes and they will lose interest in the cages?
i'm more concerned about the loud noises they can make and the fights between them around the day that can happen when they are above the cages , this is a big distraction and disturbance for any living thing who wants to breed. but i'm pretty sure the finches will be safe because all the perches are placed away from every side of the cages.
you can check the following images and see why i don't have the freedom to put the perches where i want

the front side with plastic mesh

the cages side

the walls are either windows or ceramic tiles