I hadn't thought of the Amazon shopping basket, but no, on checking it's empty.
I had thought of clearing the completed, which I did, but which didn't cure the problem.
Adding new items isn't the problem. Items do indeed appear pretty much immediately. The problem is with items I've added in the past (and that were almost certainly visible on the list at that time) but which have now become "invisible" in the app. It's like the app is treating them as though I've ticked them as completed (which I didn't do as far as I am aware) but the list on the server (the one Alexa reads out) still has them, correctly, as uncompleted.