Woodpigeons are not the same as the feral pigeons you find in town centres. They are also so crap at sitting in trees that they are rather inappropriately named, imo.
We have 2 feeders. One for seed that only small birds (mostly tits, sparrows) and the odd adventurous vole can access.
The other is a fatball feeder. We abandoned one that was like a cage because the jackdaws learned that if they hung upside down from it they could peck the balls until they were small enough to steal, much to the delight of the woodpigeons below, who are too fat and stupid to be able to use either feeder.
One like a spiral looked to be more jackdaw proof until one learned that it could push the spring apart with its feet.
Any concern about the jackdaws has been blown out of the water by the local grey squirrel, though. We were baffled on Tuesday to find the feeder on the ground, empty. Thought that the regular jackdaw vs magpie squabble might have dislodged it.
DH caught the squirrel with its arm inside the feeder, pulling out handfuls of food, this morning. It didn't even flinch when he went outside. I went out for half an hour, this morning, and came back to find it on the ground, again!