New Outlook won't let me add my outlook email account.

That worked. I had tried everything I could think of. Thank you!

I only have a btinternet.com email account and it won't let me add an outlook account

That's why you can't. Earlier gmail and outlook were linked and now due to a bug such account cannot be added. Remove the binding in aliases and your outlook will be added at the first time

I'm not trying to add a gmail account - I can't even add an outlook account to new outlook!

Solved a problem that Microsoft has not solved for 2 years, but kicks everyone to switch to a new cheesy application.
In general, the problem is that your gmail mail or some other service is not only mail, but also an alias tied to your Microsoft account. You need to go to Microsoft account settings - information - change account data - account alias - assign the alias to something else, for example outlook, and delete the gmail alias. After this manipulation you can safely log in to both gmail and outlook at the same time. Thank you microsoft for ruining the best email application by replacing it with a bunch of stinking garbage.