I logged into MyBT using my wife's mobile number.
Once in I went to 'My Details', '2 factor authentication', 'Edit' and then the only option available is to change the mobile number.
There is no option to switch 2 factor authentication on or off... nor are there currently any other options.
I then changed the phone number to my landline number.
This means that the incoming SMS message is relayed to me on the landline by voice.
This also means that when my wife's mobile is not available I can still access MyBT using my desktop computer and the landline.
Did you try checking/changing your recovery details using a web browser and not the app as I suggested in mesage 79?