I have two-factor authentication enabled on my Google account, and in order to log into my account on my iPhone one has to use the Google Smart Lock application from the iOS app store.
https://itunes.apple.com/au/app/google-smart-lock/id1152066360?mt=8
After signing in, being prompted for my 2FA device which I press, I go through the prompts, and then I am presented again with the login form.
Best Answer
The solution here was that at some point I had disabled Safari which doesn't really uninstall it as it can't be removed but does remove the app icon from your home pages. It also seems to have other effects as cookies or however the Smart Lock app is saving state fails to work, and thus will continuously ask for you to log in.
As of iOS 12, this setting is found: Settings > Screen Time > Content and Privacy Restrictions > Allowed Apps
After ensuring that I had enabled Safari, everything worked perfectly.