Hi
Unfortunately it depends entirely on who your broadband supplier is. As a previous post stated Virgin are one of the companies that let you retain access to your old mailbox. (Although mine has just been deleted as I didn't access it for some months).
However, you never actually own an e-mail address, as all you're doing when you're a customer of a broadband supplier is renting webspace from the ISP for your e-mail, which is then deleted and made available again to other customers once you leave. My advice is to get a good public e-mail such as Google Mail or MSN Hotmail which keeps you independent from any broadband supplier. They're both free, have a decent amount of mail space to offer, are accessible from anywhere in the world via a web interface, and most importantly you'll never lose it should you change supplier!
Also, they're both accessible from programs like Outlook or Thunderbird, which makes reading your e-mail easier.
Before you leave BT i would send a group mail out, back up all your historic mail, and then sign up for one of the above.