Thank you again, John Galt, and my apologies for misreading the heading of your previous reply and addressing you as 'pm'.
I don't use Gmail's 2-way authentication for my email account. That is not the source of my problem. In fact all three of my email accounts — even the BT one — are working perfectly well at the moment; the reason for my initial posting was that I have my personal way of keeping a record of my most important passwords and today discovered that I may not have kept one of the email ones up-to-date.
If I have understood you correctly, the only way to re-enter a password for an email account is to delete the account and set the account up again. My memory tells me (but it may be telling a lie) that there used to be a way of just deleting a password and typing it in again. If that has been changed by email providers and not by Apple in updates to MacOS and iOS, then it is strange that my three email accounts — gmail, bt/yahoo! internet and icloud — have all changed in this way at around the same time. I remain puzzled.