I think we might have had the same problem as in a very tall birch tree dripped a very sticky wet looking substance all over everything underneath it, bins, chairs, porch, greenhouse, paving etc. It did look like the leaves were wet, which a week or so began to drop off. I couldn't see anything at all but assumed it must have been aphids in the absence of anything else. It seems to have stopped now but the birch doesn't look very healthy. Never known it to happen before in the 11 years we've been here - interesting.
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Gardening in Central Norfolk on improved gritty moraine over chalk ... free-draining.