You've identified where the delays probably are then - in the bt mail servers.
When one of my ISPs was having problems with their mail server recently - some test emails I sent took up to a week to arrive - but they finally did - much to my confusion, as I wondered at first where they had come from!
We are on BT Broadband at the office and all e-mails come into my PC. I use Outlook here as well and there are no problems, all e-mails arrive within a short while. It's just this new connection at home that's a problem. I sent a short e-mail from the office at 5pm last night to home and it still hadn't arrived at 08.30am today. Something funny going on. Trouble is if you try and call BT you spend 3/4 hour in a ruddy call Q. I thought Telewest's response service was bad but BT's is bloody awful!!