Since you’ve already turned off the Always BBC Myself option in Settings Mail, try toggling it. Turn it on for a while and send a few test emails, then turn it off again.
If that does not work you can try Reset All Settings in Settings > General > Reset. This does not delete content, apps, or third party settings. It will put most system and native app settings back to default, so be prepared to do some tweaking afterwords.
Be careful with the Reset settings. Don’t tap the wrong one by accident.
Note: Wow, they’ve really changed up Reset settings in iPadOS 15 Public Beta. Couple of new options, and different UI.