Thanks to moderator DanielS and Patrick from BT Digital Care for resolving this issue. All my BT Mail accounts seem to have been deleted.
However, BT's server seemed to detect suspicious activity and barred me from my main BT ID. It presented me with a screen where I needed to choose new passwords for my main BT ID and each of the email accounts, but everything seems to be OK now.
I did raise a fault report, but it was only partially resolved. This was really because I was doing it on behalf of my parents, who are both over 75. If I could ask you not to telephone them again, at least not before prior arrangement with myself because it just adds to further complications & stress. Also, they are not likely to answer the call.
Maybe there's a way to arrange for you to phone me? e.g. perhaps if you were to email them & ask their permission for me to act on their behalf. I'll let them know it's ok to give you my contact details.