Just in case anyone is still struggling on alone - or being told it's their own fault.
There is a HUGE problem with BT Email at the moment - (many) thousands of customers have had no email access for over 2 days now.
It appears to be a problem with BT's American suppliers - the rumour mill says BT are moving people back to the old Yahoo system as fast as possible and that "emails will have been lost" in the process.
There is an update (in theory) here
https://www.bt.com/consumerFaultTracking/public/faults/tracking.do?pageId=31
(you need to click on the broadband and email tab)
But it tells big fat porkies (already claimed to be fixed several times then had to admit it isn't).
Good luck if you are affected - I'm not (gmail is OK), but am struggling to dig a few friends out of the hole that BT has dumped them in.