Each time I log out the system takes me to Broadband, TV Packages, TNT Sports & Mobile Deals | BT
Have you tried clearing your browser's history and cookies and are you using the "new" email log on page as per this link?
Yes I have cleared all cookies and browsing history. When I use the page in the link it tells me it is the wrong email account even though I have two accounts.
Are you able to see the email account if you log onto your MyBT then go to "Your Products" then "Email, Manage"?
I have just re-read your first post and I think I may have misunderstood what your problem is.
What do you expect to see when you log out of your email account?
When on the page that you get when you logged out have you clicked on the Email button in the menu bar at the top of the page and if so does that bring up the log on page?
When you click on the log in box does it bring up your email address or are you entering it manually?
Why does it matter what page you get when you log out?
It is your web browser that is storing the user name and password when you log on, not the computer memory.
You need to go into your browsers settings and go to the stored password section and find the stored passwords for your email accounts and delete them.
When you next log on the browser will give you the option to save theemail address and the password again and when you next log on the email addresses should be there in a drop down box and you should be able to select the one you want.