I'm sat here with
@DaveP thinking about lunch. We both wonder whether you may have multiple Google Authenticator entries for the same email address, as is commonplace and, as a result, could be picking the wrong code for Nominet? We aren't saying you're stupid, just that people make mistakes particularly when under stress (house move).
Reminds me of the old days when one had to post letters to undertake domain name transfers. Will they accept the material by email?
Obviously they don't know you and don't want to be responsible for giving someone access to your WDM while you could be out of contact on an exotic holiday in the Seychelles. Better safe than sorry?