Always happy to try where others have been successful - unfortunately a router reset made no difference and I still get the error as above.
After all my previous comments -mainly concerning the failure to access BTYahoo mail on a web page I will put on record that tonight - Sat 20 Oct 2018 - everything worked.
From Yahoo UK Home page I clicked SIGN IN and when prompted entered my @btinternet email address which took me to the BT Home page login with my email address already in situ. I added my password and - failure - message about experiencing problems and return to login
I returned to login and inserted email address and password and straight in to my BTYahoo mail platform.
The failure bit happened everytime so a bit of fine tuning needed somewhere.
I have two addresses @btinternet.com and the above worked with both of them.
Now - it is Saturday evening and not many on the Internet.
My pesimistic self says lets see what happens on Monday! I will report back.
Monday evening - 48hrs on and the system still works and, the silly little failure I noted earlier has also disappeared.
At last perhaps we are getting back to normal service.