Many thanks for the suggestions. I can confirm that the problem occurs in all the apps I have tested (Byword, Textedit, BBEdit, mail in a browser)
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I went through all the suggestions at the page @Stephen_C mentioned including resetting all permissions again and the prolem continues.
I removed all other apps from Accessibility and that did not help.
I'm going to try and restore preferences saved in Time Machine and see whether that helps, but at this point I am not hopeful.
I have also downloaded and installed the workflow to save preferences, in the faint hope that it might be something about synced preferences, and maybe that will help going forward.
Is there any point in deleting Alfred (I have 5.5) and installing everything afresh?