Following your leads, I have tracked down what happened.Without those clues< I would still be post.
Sadly, none of the messages I received from the BT system provided any useful details, starting with those anonymous error codes.
The error messages that I posted did not say something helpful like "Already assigned to a different address".
On examining the account details I saw that, as well as the main BT address that I have always used to manage BT accounts, the TV account was also associated with another email address, one that I have never used for either of my two BT accounts.
It turned out that they had different email addresses. (I wonder if that happened because back in the distant past I had to set up that sort of access to manage two different BT accounts. )
The email address for the TV account was not the same as the one for the other account.
Now I have to work out how to rationalise the arrangement.
Thanks you your guidance I now understand what is happening.
If only BT's error messages had provided useful feedback. Or, in the case of the error codes, said something, anything.