To get you over the immediate problem of inability to contact elderly parents, just create a Gmail address and use that until BT email problem is resolved.
Have you tried clearing your browser cookies and cache, have you tried a different browser.
Yes I've done all of that. And I do have a gmail account but that is not the point. I want to know what BT have done that has made my webmail which worked perfectly at 9.30am this morning be broken since then when I have done nothing.