Update: It happened again with the same character, so I went through the "fix" suggested by support. It actually worked!
This is what they suggested:
I then went back into "MSCONFIG", under "services" tab, ticked "Hide all Microsoft services" again and "enabled all" - restarted my PC again, and started Blade and Soul as normal and can still access the character.
I have no idea what I was doing, but their fix actually worked!