I’ve deleted subfolders in BT mail, but they remain in MS Outlook (imap folders) with no functionality to delete them. Why is the sync not working?
I don't use Outlook but I have found this information that may help.
Check the Outlook you have un-subscribed from the folders.
Right-click on the folder that contains the sub folders you want to delete and select IMAP folders. In the IMAP folders window, use the “Query” button to be shown additional folders. Select the relevant folders and click the Unsubscribe button.
Presumably the folders have been deleted from your BTMail account and are not showing there so if that is the case I suspect that the problem is with Outlook rather than BTMail.
Have you tried a "repair" of the Outlook files? If you do decide to try it I would make a backup of your folders before doing it.