Had this problem myself, using mail forwarded (from accounts hosted by 123-reg) to my main BT broadband account. Threads elsewhere suggested various radical options, but the easier ones to check and remedy are that the Outgoing Server tab needs to have My outgoing Server (SMTP) requires authentication ticked to yes (from Outlook Inbox select Tools menu, Account Settings..., highlight the account you're forwarding from, 'Change...', 'More Settings', Outgoing Server tab). That solved it for other people, but the one I think got me sorted was to delete all mail in the webmail account that goes with the main POP3/SMTP account I use with Outlook. I have no idea why that should affect anything, but I'm fine today having cleared it yesterday evening. BT occasionally send mails to the webmail account (which I don't otherwise use), so it's one to keep an eye on if problem recurrs. Hope this helps!
BT Outlook Network Password