Do you have the right small birds? They're not all insect eaters.
Bluetits seem to be the best for eating aphids, as others have said, and
I often see them eating aphids on the honeysuckle outside the kitchen
window.

How can you have "wrong" or "right" birds in the garden? Surely you
get what arrives don't you? You can't choose them. I can sort of see
your point though. I cannot stand magpies and chase them away at every
opportunity, so I suppose, for me, they must be the wrong birds. I do
the same with grey squirrels - nasty creatures.
John
In limine sapientiae