I discovered this morning that the Google Authenticator app is broken in iOS 7. While it does display authentication codes, it doesn’t display the associated service description. So unless you only use Authenticator for a single service, you’re kinda stuck.
Google are aware of the issue, but haven’t yet released a fix.
Urgently needing to login to Amazon AWS, I discovered an alternative app called Authy that does work on iOS 7. I was quickly able to get setup with (the better looking) Authy and Amazon AWS, Google and Dropbox, and subsequently deleted the broken Google Authenticator app.