Two work-arounds have been found, but neither seems entirely ideal and to me there still seems to be some technical issue with the launcher that needs to be resolved.
Solution 1 - Found by Premo in another comment: I linked my Gmail to my Blizzard account, and signing in using the Gmail login rather than the Username and Password got me on to the Launcher.
It’s a little silly since my login username email and gmail were exactly the same. And the fact that I needed to link an account suggests to me that the issue is with the launcher login itself.
Solution 2 - On the login screen in the Settings (cog symbol) I selected “Continue without Logging In”.
This gave me access to the launcher, and from there I could open an individual game and login on the game’s menu.
As I said these feel like workarounds rather than fixes, as I still cannot login using my default email address and password on the launcher login page. So if a fix is in the works that would be greatly appreciated still!