IMAP Accounts Won't Login

After upgrading to El Capitan, most of my IMAP mail accounts are rejected, with the prompt that I need to give my password. I do this but each account is rejected, with the message, "unable to verify login or password details".

These details haven't changed and I can still access the accounts with my android tablet, so I know the serveres for these accounts are working.

I've tried multiple restarts, checking ports and all settings multiple times and tinkering in the advanced options panel by turning the automatic setup option on and off. I've also tried deleting and re-adding one account afresh but I get the same error message. I am 100% sure the details I am giving mail about these accounts is correct, yet time after time they're rejected. The accounts all show up in the side bar (unconnected) and from what i can tell from snooping in my user library, the mailboxes themselves have transferred over, but no messages which were in the inbox appear.

My other Mac seems to have upgraded with no issues, and accounts from the same host (Dreamhost) are working without issue, so it's something specific to the upgrade process of this one mac.

I'm at my wits end with this, if anyone has any suggestions then I'm all ears, thanks.