Yes the call centre staff should be able to change the number on your BAEC account, but I'm not convinced that will feed through to the 2FA. The BAEC call staff can't change any 2FA settings. Too many examples in this thread...
https://www.flyertalk.com/forum/brit...-login-10.html
OP if you don't have any devices / app logged in, have you tried the other options below SMS for alternative 2FA?