When we set up our e-mail arrangements many years prior to the introduction of mandatory 2FA, we had a master account, based on the family surname, with subsidiary personalised accounts for each individual (there are four of us). Then came mandatory 2FA, and as far as I can make out, the only option appears to have the 6-digit codes for all five of our e-mail addresses sent to the same mobile phone number. This is most inconvenient for a busy household. Is there any way of setting the destination mobile numbers individually for each email address?
When you set up the email accounts for your family did you use the BT procedure to "gift" the email accounts to each of them? This would mean that they would have their own BTID and MyBT which they would have been able to add their contact details and mobile numbers.
I suspect that you did not do that so as far as BT are concerned the email accounts are all your and as such all using the same 2FA contact number.
If that is correct you will need to "gift" the email accounts to them and they will need to set up a BTID.
See links and sub links
Alternatively, don't use webmail, use a client/app which doesn't invoke 2FA