This finally bit me today. The app had logged me out and told me this was for my protection and I should follow the instructions in an email I should have been sent. Not possiböle as there was no email. I then tried logging in on the website, which failed as well but did at least produce the required email.
The email let me "unlock" my account. This was initially a source of some relief -- but only because I didn't know what it meant. I was able to log in on the app and confirm that my Avios are all still there. However... No such joy with the website. I can now start the login process, but fail every time on 2FA. The one-time password from my authenticator app is rejected as "invalid", as is the recovery code (which I copied and pasted into a note when I set up 2FA.
Has anyone managed to find the right department to mail or phone to sort this out? Pretty please?