You’re definitely connecting the correct HMRC account? Some people have different government gateway logins for different purposes (maybe one for your personal self assessment and another for your business taxes), and if you’re already logged in to the gateway as the wrong one when you try to make the connection in QuickFile it may not give you the opportunity to switch.
I’d start a private browser window / incognito mode / whatever it’s called in your browser, and try again from there as that definitely won’t have any saved login details or cookies (for QuickFile or for the gateway).