silver birch has sticky deposits on leaves

It sounds as if there's an aphid colony on the leaves, that would make sticky messes and drop onto the plants underneath. Have a close look to see what's on the leaves.

I agree. I have a silver birch in the back garden and the same thing happens every year.
A few years ago when hoverflies were more common they used to get rid of the aphids but now we seem to get more rain in summer the hoverflies seem to have disappeared. No idea what one can do!

I suppose a pressure washer with insecticide might help - it would reach quite hugh up the tree but I wouldn't want to do it without a mask and VERY old clothes!!!